Sosyal Bilimler için İstatik - I Statistics Practice Problems Bülent Köksal Practice Problems Stastistics for Business and Economics, 9th ed. McClave, Benson, Sincich 1 - 9 Chapter 1 Statistics, Data, and Statistical Thinking 10 - 42 Chapter 2 Methods for Describing Sets of Data 43 - 70 Chapter 3 Probability 71 - 115 Chapter 4 Discrete Random Variables 116 - 208 Chapter 5 Continuous Random Variables 209 - 237 Chapter 6 Sampling Distributions 238 - 317 Chapter 7 Inferences Based on a Single Sample: Estimation with Confidence Intervals 318 - 419 Chapter 8 Inferences Based on a Single Sample: Tests of Hypotheses 420 - 468 Chapter 9 Inferences Based on aTwo Samples: Confidence Intervals and Tests of Hypothesis 469 - 525 Chapter 10 Design of Experiments and Analysis of Variance (ANOVA) 526 - 552 Chapter 12 Simple Linear Regression 553 - 568 Chapter 13 Multiple Regression and Model Building xxx - xxx Chapter 16 Nonparametric Statistics xxx - xxx Bayesian Statistics and Decision Analysis Solve the problem. 1) What is statistics? 2) A published analysis recently stated "Based on a sample of 80 newly hired truck drivers, there is evidence to indicate that, on average, independent truck drivers are overpaid relative to company-hired truck drivers." This statement is an example of ___________. A) descriptive statistics B) a random sample C) inferential statistics D) a conclusion 3) A sample of high school teenagers reported that 96% of those sampled are interested in pursuing a college education. This statement is illustrates __________. A) descriptive statistics B) statistical inference C) sampling D) quantitative variables 4) A survey of 5000 high school students indicated that 20% of those surveyed read at least one best-seller each month. Give an example of a descriptive statement and an inferential statement that could be made based on this information. 5) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 150 students and carefully recorded their parking times. Identify the population, sample, and variable of interest to the administrators. 6) A dealership manager records the colors of automobiles on a used car lot. Identify the type of data collected A) quantitative B) qualitative 17) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. Identify the population of interest to the university administration. A) the entire set of faculty, staff, and students that park at the university B) the entire set of students that park at the university C) the 250 students from whom the data were collected D) the students that park at the university between 9 and 10 AM on Wednesdays 8) If inaccuracies exist in the values of the data recorded, what is indicated? A) nonresponse bias B) measurement error C) selection bias D) unethical statistical practice 9) What is meant by selection bias? 10) The bar graph below shows the political party affiliation of 1,000 registered U.S. voters. What percentage of the 1,000 registered U.S. voters belonged to one of the traditional two parties (Democratic and Republican)? A) 25% B) 35% C) 75% D) 40% 211) A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below. Stem Leaves 3 2 8 4 0 3 4 7 8 9 9 9 5 0 1 1 2 3 4 5 6 1 2 5 6 6 7 3 6 8 9 2 What percentage of the respondents rated overall television quality as very good (regarded as ratings of 80 and above)? A) 2% B) 8% C) 4% D) 1% 12) Fill in the blank. One advantage of the ____________ is that the actual data values are retained in the graphical summarization of the data. A) bar graph B) box plot C) stem-and-leaf plot D) pie chart 13) Which of the following explains the shape of the distribution best? A) median B) stem-and-leaf plot C) box plot D) mean 14) The scores for a statistics test are as follows: 87 76 97 77 92 94 88 85 66 89 79 99 52 90 83 88 82 57 10 69 Create a stem-and-leaf display for the data. 15) A data set contains the observations 7, 6, 5, 3, 4. Find x ? . A) 21 B) 2520 C) 25 D) 11 16) A data set contains the observations 2, 7, 3, 6, 5. Find x ? 2 . A) 46 B) 23 C) 123 D) 529 17) A data set contains the observations 3, 1, 5, 6, 4. Find x ? 2 . A) 38 B) 19 C) 87 D) 361 18) A data set contains the observations 8, 1, 3, 4, 6. Find (x - 5) ? . A)-2 B) 47 C) 12 D)-3 19) A data set contains the observations 3, 6, 7, 2, 8. Find x ? 2 - x ? 2 5 . A) 26.8 B) 297.2 C) 129.6 D) 540.8 320) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 97 miles per hour. Suppose that the statistician indicated that the serve speed distribution was skewed to the left. Which of the following values is most likely the value of the median serve speed? A) 92 mph B) 87 mph C) 102 mph D) 97 mph 21) A sociologist recently conducted a survey of senior citizens whose net worth is too high to qualify for Medicaid but who have no private health insurance. The ages of 25 uninsured senior citizens were as follows: 71 76 69 79 89 77 64 92 68 93 72 95 79 65 84 66 71 84 73 76 63 90 78 67 85 Find the median of the observations. A) 77 B) 76.5 C) 73 D) 76 22) The output below computed the mean and median for the national dropout rates for high school students in 1998 and 2002. Drop 1998 Drop 2002 N 51 51 MEAN 28.32 26.38 MEDIAN 27.98 25.64 Interpret the 2002 median dropout rate of 25.64. A) The average dropout rate of the 51 states was 25.64%. B) The most frequently observed dropout rate of the 51 states was 25.64%. C) Half of the 51 states had a dropout rate of 25.64%. D) Half of the 51 states had a dropout rate below 25.64%. 23) The distribution of salaries of professional basketball players is skewed to the right. Which measure of central tendency would be the best measure to determine the location of the center of the distribution? A) median B) range C) mean D) mode 424) For the distribution drawn here, identify the mean, median, and mode. A) A = mode, B = median, C = mean B) A = median, B = mode, C = mean C) A = mean, B = mode, C = median D) A = mode, B = mean, C = median 25) In skewed-right distributions, what is the relationship of the mean, median, and mode? A) mode > mean > median B) median > mean > mode C) mode > median > mode D) mean > median > mode 26) Which of the following measures the center of a distribution? A) range B) standard deviation C) median D) percentile 27) Each year advertisers spend billions of dollars purchasing commercial time on network sports television. In the first 6 months of 2001, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, listed the top 10 leading spenders (in million of dollars): Company A $71.2 Company F $27.4 Company B 63.5 Company G 26.8 Company C 57.8 Company H 21.7 Company D 57.4 Company I 23.1 Company E 30.6 Company J 19.6 Calculate the sample variance. A) 1948.697 B) 2174.580 C) 400.359 D) 3939.932 28) Last year batting averages in the National League averaged .267 with a high of .332 and a low of .217 (minimum 250 at-bats). Based on this information, which measure of variation could be calculated? A) standard deviation B) range C) percentile D) variance 29) The top speeds for a sample of five new automobile brands are listed below. Calculate the standard deviation of the speeds. 190, 100, 120, 135, 180 A) 232.5134 B) 166.5683 C) 38.7298 D) 100.00 530) Various state and national automobile associations regularly survey gasoline stations to determine the current retail price of gasoline. Suppose one such national association decides to survey 200 stations in the United States and intends to determine the price of regular unleaded gasoline at each station. In the context of this problem, define the following descriptive measures: µ, ?, x, s 31) Calculate the standard deviation of a sample for which n = 6, x ? 2 = 830, x ? = 60. A) 6.78 B) 164.00 C) 6.19 D) 46.00 32) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 96 miles per hour (mph) and the standard deviation of the serve speeds was 13 mph. If nothing is known about the shape of the distribution, give an interval that will contain the speeds of at least three-fourths of the player's serves. A) 83 mph to 109 mph B) 122 mph to 148 mph C) 70 mph to 122 mph D) 57 mph to 135 mph 33) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 100 miles per hour (mph) and the standard deviation of the serve speeds was 8 mph. Assume that the statistician also gave us the information that the distribution of the serve speeds was mound-shaped and symmetric. What proportion of the player's serves was between 116 mph and 124 mph? A) 0.997 B) 0.047 C) 124 D) 0.0235 34) The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 300 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watched television. The mean and the standard deviation for their responses were 12 and 3, respectively. PAWT constructed a stem-and-leaf display for the data that showed that the distribution of times was a symmetric, mound-shaped distribution. Give an interval where you believe most (approximately 95%) of the television viewing times fell in the distribution. A) between 3 and 21 hours per week B) less than 9 and more than 15 hours per week C) between 6 and 18 hours per week D) less than 18 35) By law, a box of cereal labeled as containing 32 ounces must contain at least 32 ounces of cereal. It is known that the machine filling the boxes produces a distribution of fill weights with a mean equal to the setting on the machine and with a standard deviation equal to 0.02 ounce. To ensure that most of the boxes contain at least 32 ounces, the machine is set so that the mean fill per box is 32.06 ounces. Assuming nothing is known about the shape of the distribution, what can be said about the proportion of cereal boxes that contain less than 32 ounces. A) The proportion is less than 2.5%. B) The proportion is at most 11%. C) The proportion is at most 5.5%. D) The proportion is at least 89%. 36) Solar energy is considered by many to be the energy of the future. A recent survey was taken to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $127 and a standard deviation of $15. If nothing is known about the shape of the distribution, what percentage of homes will have a monthly utility bill of less than $97? A) at most 25% B) at least 75% C) at least 88.9% D) at most 11.1% 37) Fill in the blank. ____________ gives us a method of interpreting the standard deviation that applies to any data set, regardless of the shape of the distribution. A) both a and b B) The Empirical Rule C) neither a nor b D) Chebyshev's rule 638) Fill in the blank. ____________ is a method of interpreting the standard deviation that applies to data that have a mound-shaped, symmetric distribution. A) Chebyshev's rule B) The Empirical Rule C) both a and b D) neither a nor b 39) To what type of data can Chebyshev's rule be applied? A) skewed-left data B) skewed-right data C) symmetric data D) all of the above 40) If nothing is known about the shape of a distribution, what percentage of the observations fall within 2 standard deviations of the mean? A) approximately 5% B) approximately 95% C) at least 75% D) at most 25% 41) What can be a source of distortion in interpreting a statistical graph? 42) Describe methods to avoid graphical distortion? 43) Which of the following probabilities for the sample points A, B, and C could be true if A, B, and C are the only sample points in an experiment? A) P(A) = 1/10, P(B) = 1/6, P(C) = 1/2 B) P(A) = 1/8, P(B) = 1/8, P(C) = 1/8 C) P(A) = 0, P(B) = 1/10, P(C) = 9/10 D) P(A) = -1/4, P(B) = 1/2, P(C) = 3/4 44) The Department of Transportation classified vehicle-to-vehicle accidents in the following manner: Accident Probability Car to Car 0.55 Car to Truck 0.16 Truck to Truck 0.29 Find the probability that a recently occurring accident involved a car. 45) A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below: Number of Vehicles Involved Did Alcohol Play a Role? 1 2 3 or more Totals Yes 55 100 15 170 No 26 172 32 230 Totals 81 272 47 400 What proportion of the accidents involved a single car without the effect of alcohol? 746) The manager of a used car lot took inventory of the automobiles on his lot and constructed the following table based on the age of his car and its make (foreign or domestic): Age of Car (in years) Make 0 - 2 3 - 5 6 - 10 over 10 Total Foreign 38 21 12 29 100 Domestic 35 25 15 25 100 Total 73 46 27 54 200 What proportion of the cars are older than 5 years old? A) 25/200 B) 81/200 C) 54/200 D) 29/200 47) A hospital reports that two patients have been admitted who have contracted Cronne's disease. Suppose our experiment consists of observing whether the patients survive or die as a result of the disease. The simple events and probabilities of their occurrence are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc.). Simple Events Probabilities SS 0.52 SD 0.14 DS 0.15 DD 0.19 Find the probability that at least one of the patients does not survive the disease. A) 0.48 B) 0.14 C) 0.29 D) 0.19 48) Fill in the blank. A(n) ______ is the process that leads to a single outcome that cannot be predicted with certainty. A) sample point B) sample space C) event D) experiment 49) Fill in the blank. A(n) __________ is the most basic outcome of an experiment. A) sample space B) sample point C) experiment D) event 50) Fill in the blank. A(n) __________ is the collection of all the sample points in an experiment. A) sample space B) event C) Venn diagram D) union 51) Fill in the blank. A(n) __________ is a collection of sample points. A) Venn diagram B) experiment C) sample space D) event (Situation Q) A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members regularly use each facility. A survey of the membership indicates that 70% regularly use the golf course, 50% regularly use the tennis courts, 25% regularly use both the golf and tennis facilities, and 5% use neither of these facilities regularly. 52) What percentage of the 600 use at least one of the golf or tennis facilities? A) .95 B) .75 C) 1.20 D) .25 53) Given that a randomly selected member uses the tennis courts regularly, find the probability that he also uses the golf course regularly. A) .357 B) .500 C) .583 D) .714 8Solve the problem. 54) The managers of a Fortune 500 company were surveyed to determine the background that leads to a successful manager. Each manager was rated as being either a good, fair, or poor manager by his/her boss. The manager's educational background was also noted. The data appear below: Educational Background Manager Rating H. S. Degree Some College College Degree Master's or Ph.D. Totals Good 2 8 21 8 39 Fair 6 17 44 20 87 Poor 9 7 5 13 34 Totals 17 32 70 41 160 What proportion of the managers had earned at least one college degree? A) 70/160 B) 111/160 C) 41/160 D) 49/160 55) The breakdown of workers in a particular state according to their political affiliation and type of job held is shown here. Suppose a worker is selected at random within the state and the worker's political affiliation and type of job are noted. Political Affiliation Republican Democrat Independent White collar 18% 5% 13% Type of job Blue Collar 14% 19% 31% Find the probability the worker is a white collar worker affiliated with the Democratic Party. A) 0.55 B) 0.05 C) 0.24 D) 0.36 (Situation R) A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members regularly use each facility. A survey of the membership indicates that 70% regularly use the golf course, 50% regularly use the tennis courts, 25% regularly use both the golf and tennis facilities, and 5% use neither of these facilities regularly. 56) Draw a Venn Diagram for this problem. Solve the problem. 57) Fill in the blank. The __________ of an event A is the event that A does not occur. A) union B) intersection C) Venn diagram D) complement 958) The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor of a company's success has been proven time and again to be customer service. A study was conducted to study the customer satisfaction levels for one overnight shipping business. In addition to the customer's satisfaction level, the customers were asked how often they used overnight shipping. The results are shown below in the following table: Frequency of Use High Satisfaction level Medium Low TOTAL < 2 per month 250 140 10 400 2 - 5 per month 140 55 5 200 > 5 per month 70 25 5 100 TOTAL 460 220 20 700 If a customer were selected at random, what is the chance that they would use the company more than five times per month or have a low level of satisfaction? A) 5/700 B) 585/700 C) 115/700 D) 120/700 59) The manager of a used car lot took inventory of the automobiles on his lot and constructed the following table based on the age of his car and its make (foreign or domestic): Age of Car (in years) Make 0 - 2 3 - 5 6 - 10 over 10 Total Foreign 38 26 15 21 100 Domestic 40 30 13 17 100 Total 78 56 28 38 200 If a car were randomly selected from the lot, what is the probability that it is either a foreign car or less than 3 years old? A) 38/200 B) 78/200 C) 140/200 D) 100/200 Answer the question True or False. 60) If two events, A and B, are mutually exclusive, then P(A and B) = P(A) × P(B). Solve the problem. 61) A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members regularly use each facility. A survey of the membership indicates that 61% regularly use the golf course, 50% regularly use the tennis courts, and 7% use neither of these facilities regularly. Find the probability that a randomly selected member uses the golf or tennis facilities regularly. 1062) A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below: Number of Vehicles Involved Did Alcohol Play a Role? 1 2 3 or more Totals Yes 58 91 21 170 No 26 174 30 230 Totals 84 265 51 400 Given that an accident involved multiple vehicles, what what is the probability that it involved alcohol? A) 112/316 B) 21/51 C) 112/400 D) 21/400 63) The manager of a used car lot took inventory of the automobiles on his lot and constructed the following table based on the age of his car and its make (foreign or domestic): Age of Car (in years) Make 0 - 2 3 - 5 6 - 10 over 10 Total Foreign 41 27 10 22 100 Domestic 38 22 13 27 100 Total 79 49 23 49 200 A car was randomly selected from the lot. Given that the car selected was a foreign car, what is the probability that it was older than 2 years old? A) 41/121 B) 59/100 C) 59/121 D) 41/100 Answer the question True or False. 64) The conditional probability of event A given that event B has occurred is written as P(B | A). Solve the problem. 65) A human gene carries a certain disease from the mother to the child with a probability rate of 35%. That is, there is a 35% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has four children. Assume that the infections of the four children are independent of one another. Find the probability that all four of the children get the disease from their mother. A) 0.179 B) 0.015 C) 0.096 D) 0.985 66) A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.97, P(C) = 0.93, and P(D) = 0.99. Find the probability that the machine works properly. A) 0.8931 B) 0.1337 C) 0.875 D) 0.8663 67) Suppose a basketball player is an excellent free throw shooter and makes 94% of his free throws (i.e., he has a 94% chance of making a single free throw). Assume that free throw shots are independent of one another. Suppose this player gets to shoot four free throws. Find the probability that he makes four consecutive free throws. A) 0.7807 B) 0.2193 C) 1 D) 0 68) Classify the events as dependent or independent. Events A and B where P(A) = 0.4, P(B) = 0.3, and P(A and B) = 0.12 A) independent B) dependent 1169) Classify the events as dependent or independent. Events A and B where P(A) = 0.1, P(B) = 0.6, and P(A and B) = 0.05 A) independent B) dependent Answer the question True or False. 70) Two events, A and B, are independent if P(A and B) = P(A) × P(B). Solve the problem. 71) Classify the following random variable according to whether it is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day A) continuous B) discrete 72) Classify the following random variable according to whether it is discrete or continuous. The speed of a car on a Los Angeles freeway during rush hour traffic A) continuous B) discrete 73) Consider the given discrete probability distribution when answering the following question. Find the probability that x exceeds 5. x 3 5 6 8 P(x) 0.11 ? 0.12 0.1 A) 0.67 B) 0.78 C) 0.22 D) 0.89 74) The Fresh Oven Bakery knows that the number of pies sold each day varies from day to day. The owner believes that on 50% of the days she sells 100 pies. On another 25% of the days she sells 150 pies, and she sells 200 pies on the remaining 25% of the days. To make sure she has enough product, the owner bakes 200 pies each day at a cost of $1.50 each. Assume any pies that go unsold are thrown out at the end of the day. If she sells the pies for $5 each, find the probability distribution for her daily profit. A) Profit P(profit) $300 .5 $550 .25 $800 .25 B) Profit P(profit) $200 .5 $450 .25 $700 .25 C) Profit P(profit) $500 .5 $750 .25 $1000 .25 D) Profit P(profit) $350 .5 $525 .25 $700 .25 75) A lab orders a shipment of 100 frogs a week, 52 weeks a year, from a frog supplier for experiments that the lab conducts. Prices for each weekly shipment of frogs follow the distribution below: Price $10.00 $12.50 $15.00 Probability 0.35 0.3 0.35 How much should the lab budget for next year's frog orders assuming this distribution does not change. (Hint: find the expected price.) A) $1250.00 B) $12.50 C) $3,380,000.00 D) $650.00 1276) A lab orders a shipment of 100 frogs a week, 52 weeks a year, from a frog supplier for experiments that the lab conducts. Prices for each weekly shipment of frogs follow the distribution below: Price $10.00 $12.50 $15.00 Probability 0.2 0.15 0.65 Suppose the mean cost of the frogs turned out to be $13.63 per week. Interpret this value. A) The median cost for the distribution of frog costs is $13.63. B) Most of the weeks resulted in frog costs of $13.63. C) The average cost for all weekly frog purchases is $13.63. D) The frog cost that occurs more often than any other is $13.63. 77) Mamma Temte bakes six pies a day that cost $2 each to produce. On 23% of the days she sells only two pies. On 10% of the days, she sells 4 pies, and on the remaining 67% of the days, she sells all six pies. If Mama Temte sells her pies for $5 each, what is her expected profit for a day's worth of pies? [Assume that any leftover pies are given away.] A)-$7.00 B) $24.40 C)-$7.12 D) $12.40 78) The random variable x represents the number of boys in a family of three children. Assuming that boys and girls are equally likely, find the mean and standard deviation for the random variable x. A) mean: 1.50; standard deviation: 0.76 B) mean: 1.50; standard deviation: 0.87 C) mean: 2.25; standard deviation: 0.87 D) mean: 2.25; standard deviation: 0.76 79) The random variable x represents the number of tests that a patient entering a hospital will have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x. x 0 1 2 3 4 P(x) 3 17 5 17 6 17 2 17 1 17 A) mean: 3.72; standard deviation: 2.52 B) mean: 1.59; standard deviation: 3.72 C) mean: 2.52; standard deviation: 1.93 D) mean: 1.59; standard deviation: 1.09 80) From the probability distribution, find the mean and standard deviation for the random variable x, which represents the number of cars per household in a town of 1000 households. x P(x) 0 0.125 1 0.428 2 0.256 3 0.108 4 0.083 Answer the question True or False. 81) The expected value of a discrete random variable must be one of the values in which the random variable can result. Solve the problem. 82) The probability that an individual is left-handed is 0.18. In a class of 80 students, what is the mean and standard deviation of the number of left-handers in the class? A) mean: 14.4; standard deviation: 3.44 B) mean: 80; standard deviation: 3.79 C) mean: 14.4; standard deviation: 3.79 D) mean: 80; standard deviation: 3.44 1383) A journal polled its readers to determine the proportion of wives who, if given a second chance, would marry their husband. According to the responses from the survey, 75% of wives would marry their husbands again. Suppose a random and independent sample of n = 12 wives was collected. Define the random variable X as the number of the 12 wives who would marry their husbands again. Then we know X is a binomial random variable. Find the probability that at most 11 of the wives sampled said they would marry their husbands again. A) 1.000000 B) 0.126705 C) 0.031676 D) 0.968324 84) The on-line access computer service industry is growing at an extraordinary rate. Current estimates suggest that only 31% of the home-based computers have access to on-line services. This number is expected to grow quickly over the next five years. Suppose 25 people with home-based computers were randomly and independently sampled. Find the probability that fewer than three of those sampled currently have access to on-line services. A) 0.018282 B) 0.006812 C) 0.005667 D)-0.006625 85) A literature professor decides to give a 12-question true-false quiz. She wants to choose the passing grade such that the probability of passing a student who guesses on every question is less than .10. What score should be set as the lowest passing grade? A) 10 B) 9 C) 7 D) 8 86) A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 35% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled. Assuming the paper's claim is correct, find the probability that more than eight but fewer than 12 of the 20 sampled believe the company's president possesses low ethical standards. A) 0.392728 B) 0.296992 C) 0.218043 D) 0.149429 87) An automobile manufacturer has determined that 30% of all gas tanks that were installed on its 1988 compact model are defective. If 14 of these cars are independently sampled, what is the probability that more than half need new gas tanks? 88) A new drug has been synthesized that is designed to reduce a person's blood pressure. Twelve randomly selected hypertensive patients receive the new drug. Suppose the probability that a hypertensive patient's blood pressure drops if he or she is untreated is 0.5. Then what is the probability of observing 10 or more blood pressure drops in a random sample of 12 treated patients if the new drug is in fact ineffective in reducing blood pressure? 89) The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 5. Find the probability that exactly six road construction projects are currently taking place in this city. A) 0.072770 B) 0.146223 C) 0.160623 D) 0.322754 90) The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 2. Find the probability that more than four road construction projects are currently taking place in the city. A) 0.857123 B) 0.142877 C) 0.947347 D) 0.052653 91) The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.8. Find the probability that less than three accidents will occur next month on this stretch of road. A) 0.992686 B) 0.007314 C) 0.024434 D) 0.975566 1492) The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.6. Find the probability of observing exactly four accidents on this stretch of road next month. A) 114.901785 B) 4.174502 C) 1.154974 D) 0.041961 93) The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 7.7. Find the probability that the next two months will both result in three accidents each occurring on this stretch of road. A) 0.001187 B) 0.000125 C) 0.068910 D) 0.034455 94) Suppose the number of babies born during an 8-hour shift at a hospital's maternity wing follows a Poisson distribution with a mean of 5 an hour. Find the probability that three babies are born during a particular 1-hour period in this maternity wing. A) 0.002053 B) 0.017547 C) 0.021780 D) 0.140374 95) Suppose the number of babies born during an 8-hour shift at a hospital's maternity wing follows a Poisson distribution with a mean of 2 an hour. Some people believe that the presence of a full moon increases the number of births that take place. Suppose during the presence of a full moon, County Hospital experienced eight consecutive hours with more than three births. Based on this fact, comment on the belief that the full moon increases the number of births. A) The belief is not supported as the probability of observing this many births is 0.000000175. B) The belief is supported as the probability of observing this many births would be 0.000000175. C) The belief is supported as the probability of observing this many births would be 0.143. D) The belief is not supported as the probability of observing this many births is 0.143. 96) The university policy department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 5.5 tickets per day. Find the probability that less than six tickets are written on a randomly selected day from this distribution. A) 0.471081 B) 0.528919 C) 0.686036 D) 0.313964 97) The university policy department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 8.9 tickets per day. Find the probability that exactly four tickets are written on a randomly selected day from this distribution. A) 4.788184 B) 174.158539 C) 0.035656 D) 1.296886 98) The university policy department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 8.5 tickets per day. Interpret the value of the mean. A) If we sampled all days, the arithmetic average number of tickets written would be 8.5 tickets per day. B) Half of the days have less than 8.5 tickets written and half of the days have more than 8.5 tickets written. C) The mean has no interpretation since 0.5 ticket can never be written. D) The number of tickets that is written most often is 8.5 tickets per day. 99) The number of goals scored at State College hockey games follows a Poisson distribution with a mean of 6 goals per game. Find the probability that a randomly selected State College hockey game would have more than three goals scored. A) 0.061969 B) 0.938031 C) 0.151204 D) 0.848796 15100) The number of goals scored at State College hockey games follows a Poisson distribution with a mean of 5 goals per game. Find the probability that each of four randomly selected State College hockey games resulted in three goals being scored. A) 0.56149561 B) 0.00540243 C) 0.00038828 D) 0.43850439 101) A small life insurance company has determined that on the average it receives 3 death claims per day. Find the probability that the company receives at least seven death claims on a randomly selected day. 102) The number of traffic accidents that occurs on a particular stretch of road during a month follows a Poisson distribution with a mean of 7.8. Find the probability that less than two accidents will occur on this stretch of road during a randomly selected month. 103) Suppose the number of babies born during an eight-hour shift at a hospital's maternity wing follows a Poisson distribution with a mean of 6 an hour. Find the probability that exactly five babies are born during a randomly selected hour. 104) Suppose x is a random variable for which a Poisson probability distribution with ? = 6.5 provides a good characterization. Find µ for x. A) 6.5 B) 42.25 C) 3.3 D) 6.5 105) Suppose x is a random variable for which a Poisson probability distribution with ? = 4.6 provides a good characterization. Find ? for x. A) 2.3 B) 4.6 C) 21.16 D) 4.6 106) Suppose that 4 out of 15 liver transplants done at a hospital will fail within a year. Consider a random sample of 3 of these 15 patients. What is the probability that all 3 patients will result in failed transplants? A) 0.008791 B) 0.733333 C) 0.266667 D) 0.75 107) Suppose that 5 out of 11 liver transplants done at a hospital will fail within a year. Consider a random sample of 4 of these 11 patients. Find the probability that at least one of the 4 patients will result in a failed transplant? A) 0.30303 B) 0.045455 C) 0.25 D) 0.954545 108) Suppose the candidate pool for two appointed positions includes 12 women and 14 men. All candidates were told that the positions were randomly filled. Identify the probability distribution that models the number of males appointed to the positions. A) normal B) binomial C) hypergeometric D) poisson 109) Suppose the candidate pool for two appointed positions includes 8 women and 5 men. All candidates were told that the positions were randomly filled. Find the probability that two men are selected to fill the appointed positions. A) 0.358974 B) 0.25641 C) 0.128205 D) 0.153846 110) As part of a promotion, both you and your roommate are given free cellular phones from a batch of 65 phones. Unknown to you, five of the phones are faulty and do not work. What type of probability distribution describes the number of the two phones (yours and your roommates) that are faulty? A) hypergeometric B) binomial C) uniform D) poisson 16111) As part of a promotion, both you and your roommate are given free cellular phones from a batch of 14 phones. Unknown to you, six of the phones are faulty and do not work. Find the probability that one of the two phones is faulty. A) 0.692308 B) 0.263736 C) 0.527473 D) 0.164835 112) Suppose that 4 out of 11 liver transplants done at a hospital will fail within a year. Consider a random sample of 4 of these 11 patients. What is the probability that none of the 4 patients will result in a failed transplant? 113) As part of a promotion, both you and your roommate are given free cellular phones from a batch of 14 phones. Unknown to you, five of the phones are faulty and do not work. Find the probability that you and your roommate's phones are both faulty. 114) Given that x is a hypergeometric random variable with N = 23, n = 8, and r = 8, compute the mean of x. A) 23 B) 0.348 C) 2.783 D) 1 115) Given that x is a hypergeometric random variable with N = 16, n = 7, and r = 10, compute the variance of x. A) 4.375 B) 2.092 C) 0.128 D) 0.984 Answer the question True or False. 116) The number of children in a family can be modelled using a continuous random variable. 117) For any continuous probability distribution, P(x = c) = 0 for all values of c. Solve the problem. 118) High temperatures in a certain city for the month of August follow a uniform distribution over the interval 60°F to 93°F. What is the probability that a randomly selected August day has a high temperature that exceeded 65°F? A) 0.8485 B) 0.0303 C) 0.4248 D) 0.1515 119) High temperatures in a certain city for the month of August follow a uniform distribution over the interval 63°F to 93°F. Find the high temperature which 90% of the August days exceed. A) 90°F B) 66°F C) 73°F D) 93°F 120) The diameter of ball bearings produced in a manufacturing process can be explained using a uniform distribution over the interval 7.5 to 9.5 millimeters. What is the mean diameter produced in this manufacturing process? A) 9.0 millimeters B) 9.5 millimeters C) 8.0 millimeters D) 8.5 millimeters 121) The diameter of ball bearings produced in a manufacturing process can be explained using a uniform distribution over the interval 2.5 to 4.5 millimeters. What is the probability that a randomly selected ball bearing has a diameter greater than 3.1 millimeters? A) 0.6889 B) 0.7 C) 0.4429 D) 1.5 122) The diameter of ball bearings produced in a manufacturing process can be explained using a uniform distribution over the interval 6.5 to 8.5 millimeters. Any ball bearing with a diameter of over 8.25 millimeters or under 6.75 millimeters is considered defective. What is the probability that a randomly selected ball bearing produced is defective? A) 0 B) .50 C) .25 D) .75 17123) Suppose x is a uniform random variable with c = 30 and d = 80. Find the standard deviation of x. A) ? = 2.04 B) ? = 31.75 C) ? = 3.03 D) ? = 14.43 124) Suppose x is a uniform random variable with c = 10 and d = 90. Find the probability that a randomly selected observation exceeds 42. A) 0.6 B) 0.9 C) 0.1 D) 0.4 125) Suppose x is a uniform random variable with c = 10 and d = 50. Find the probability that a randomly selected observation is between 13 and 45. A) 0.80 B) 0.20 C) 0.8 D) 0.5 126) A machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 8.5 to 11.5 gallons per minute. Find the variance of the distribution. A) 33.33 B) 0.75 C) 6.75 D) 0.33 127) A machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 8.5 to 10.5 gallons per minute. What is the probability that at the time the machine is checked it is pumping more than 9.5 gallons per minute? A) .50 B) .7692 C) .25 D) .667 128) A machine is set to pump cleanser into a process at the rate of 6 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 6.0 to 7.0 gallons per minute. Would you expect the machine to pump more than 6.95 gallons per minute? A) Yes, since .05 is a high probability. B) No, since .05 is a low probability. C) Yes, since .95 is a high probability. D) No, since .95 is a high probability. 129) A machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 8.5 to 11.5 gallons per minute. Find the probability that between 9.0 gallons and 10.0 gallons are pumped during a randomly selected minute. A) 0.33 B) 0 C) 0.67 D) 1 130) Suppose a uniform random variable can be used to describe the outcome of an experiment with the outcomes ranging from 10 to 70. What is the mean outcome of this experiment? A) 45 B) 40 C) 70 D) 10 131) Suppose a uniform random variable can be used to describe the outcome of an experiment with the outcomes ranging from 20 to 80. What is the probability that this experiment results in an outcome less than 30? A) 1 B) 0.25 C) 0.17 D) 0.1 132) High temperatures in a certain city for the month of August follow a uniform distribution over the interval 145°F to 165°F. What is the probability that a randomly selected August day has a high temperature that exceeded 150°F? 133) The diameter of ball bearings produced in a manufacturing process can be explained using a uniform distribution over the interval 3.5 to 9.5 millimeters. What is the probability of a randomly selected ball bearing having a diameter less than 5.5 millimeters? 18134) Suppose x is a uniform random variable with c = 10 and d = 80. Find the mean of the random variable x. 135) A machine is set to pump cleanser into a process at the rate of 7 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 6.5 to 7.5 gallons per minute. Find the probability that the machine pumps less than 6.75 gallons during a randomly selected minute. 136) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 50 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 345 seconds. A) .0107 B) .9893 C) .5107 D) .4893 137) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 60 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association? A) 361.3 seconds B) 558.7 seconds C) 536.8 seconds D) 383.2 seconds 138) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 50 seconds. Between what times do we expect most (approximately 95%) of the boys to run the mile? A) between 377.75 and 542.28 seconds B) between 365 and 555 seconds C) between 362 and 558 seconds D) between 0 and 542.28 seconds 139) The amount of corn chips dispensed into a 48-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 48.5 ounces and a standard deviation of 0.2 ounce. What proportion of the 48 ounce bags contain more than the advertised 48 ounces of chips? A) 0.4938 B) 0.5062 C) 0.0062 D) 0.9938 140) The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a mean of 12.54 ounces and a standard deviation of 0.36 ounce. The cans only hold 12.90 ounces of soda. Every can that has more than 12.90 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. What is the probability a randomly selected can will need to go through this process? A) .8413 B) .1587 C) .6587 D) .3413 141) A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was installed, the amount being spent on personal calls followed a normal distribution with an average of $500 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Using the distribution above, what is the probability that a randomly selected month had a PCE of between $375.00 and $590.00? A) .9579 B) .0001 C) .9999 D) .0421 19142) A company conducted a study and determined it had $4900 of preventable monthly loss, with a normal distribution and a standard deviation of $50. A new policy was put into place, and the preventable loss the next month was $4600. What inference can you make about the new policy? A) While the probability the monthly loss would be as low as $4600 is small, it is not unexpected. B) Because the probability the monthly loss would be as low as $4600 is not very small, the new policy is not working. C) The new policy is probably less effective than the one it replaced. D) Because the probability the monthly loss would be as low as $4600 is small, the new policy is working. 143) A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was installed, the amount being spent on personal calls follows a normal distribution with an average of $700 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Find the probability that a randomly selected month had a PCE that falls below $550. A) 0.9987 B) 0.7857 C) 0.0013 D) 0.2143 144) The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2800 miles. What is the probability a particular tire of this brand will last longer than 57,200 miles? A) .2266 B) .1587 C) .8413 D) .7266 145) A firm believes the internal rate of return for its proposed investment can best be described by a normal distribution with mean 35% and standard deviation 3%. What is the probability that the internal rate of return for the investment will be at least 30.5%? 146) Use the standard normal distribution to find P(0 < z < 2.25). A) 0.4878 B) 0.5122 C) 0.7888 D) 0.8817 147) Use the standard normal distribution to find P(-2.25 < z < 0). A) 0.6831 B) 0.5122 C) 0.4878 D) 0.0122 148) Use the standard normal distribution to find P(-2.25 < z < 1.25). A) 0.8944 B) 0.4878 C) 0.8822 D) 0.0122 149) Use the standard normal distribution to find P(-2.50 < z < 1.50). A) 0.6167 B) 0.5496 C) 0.8822 D) 0.9270 150) Use the standard normal distribution to find P(z < -2.33 or z > 2.33). A) 0.0198 B) 0.0606 C) 0.7888 D) 0.9809 151) Find a value of the standard normal random variable z, called z 0 , such that P(-z 0 ? z ? z 0 ) = 0.98. A) 1.645 B) 2.33 C) 1.96 D) 0.99 152) Find a value of the standard normal random variable z, called z 0 , such that P(z ? z 0 ) = 0.70. A)-0.81 B)-0.47 C)-0.98 D)-0.53 153) Find a value of the standard normal random variable z, called z 0 , such that P(z ? z 0 ) = 0.70. A) 0.98 B) 0.53 C) 0.47 D) 0.81 20154) Suppose a random variable x is best described by a normal distribution with µ = 60 and ? = 12. Find the z-score that corresponds to the value x = 72. A) 5 B) 12 C) 1 D) 72 155) Suppose a random variable x is best described by a normal distribution with µ = 60 and ? = 3. Find the z-score that corresponds to the value x = 72. A) 5 B) 12 C) 3 D) 4 156) Suppose a random variable x is best described by a normal distribution with µ = 60 and ? = 10. Find the z-score that corresponds to the value x = 60. A) 0 B) 6 C) 10 D) 1 157) Suppose a random variable x is best described by a normal distribution with µ = 60 and ? = 8. Find the z-score that corresponds to the value x = 30. A)-3.75 B) 3.75 C) 8 D)-8 158) IQ test scores are normally distributed with a mean of 103 and a standard deviation of 11. An individual's IQ score is found to be 104. Find the z-score corresponding to this value. A)-11.00 B) 0.09 C) 11.00 D)-0.09 159) A firm believes the internal rate of return for its proposed investment can best be described by a normal distribution with mean 23% and standard deviation 3%. What is the probability that the internal rate of return for the investment exceeds 29%? 160) The board of examiners that administers the real estate broker's examination in a certain state found that the mean score on the test was 490 and the standard deviation was 72. If the board wants to set the passing score so that only the best 10% of all applicants pass, what is the passing score? Assume that the scores are normally distributed. 161) The board of examiners that administers the real estate broker's examination in a certain state found that the mean score on the test was 410 and the standard deviation was 72. If the board wants to set the passing score so that only the best 80% of all applicants pass, what is the passing score? Assume that the scores are normally distributed. 162) The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 5500 miles. If the manufacturer guarantees the tread life of the tires for the first 53,400 miles, what proportion of the tires will need to be replaced under warranty? 163) Farmers often sell fruits and vegetables at roadside stands during the summer. One such roadside stand has a daily demand for tomatoes that is approximately normally distributed with a mean equal to 538 tomatoes per day and a standard deviation equal to 30 tomatoes per day. If there are 496 tomatoes available to be sold at the roadside stand at the beginning of a day, what is the probability that they will all be sold? 164) Farmers often sell fruits and vegetables at roadside stands during the summer. One such roadside stand has a daily demand for tomatoes that is approximately normally distributed with a mean equal to 135 tomatoes per day and a standard deviation equal to 30 tomatoes per day. How many tomatoes must be available on any given day so that there is only a 1.5% chance that all tomatoes will be sold? 21165) You are performing a study about the weight of preschoolers. A previous study found the weights to be normally distributed with a mean of 30 and a standard deviation of 4. You randomly sample 30 preschool children and find their weights to be as follows. 25 25 26 26.5 27 27 27.5 28 28 28.5 29 29 30 30 30.5 31 31 32 32.5 32.5 33 33 34 34.5 35 35 37 37 38 38 Draw a histogram to display the data. Is it reasonable to assume that the weights are normally distributed? Why? 166) Which of the following statements is not a property of the normal curve? A) symmetric about µ B) P(µ - 3? < x < µ + 3?) ? .997 C) P(µ - ? < x < µ + ?) ? .95 D) mound-shaped (or bell shaped) 167) Which one of the following is not a method used for determining whether data are from an approximately normal distribution? A) Construct a normal probability plot. The points should fall approximately on a straight line. B) Compute the intervals x ± s, x ± 2s, and x ± 3s. The percentages of measurements falling in each should be approximately 68%, 95%, and 100% respectively. C) Find the interquartile range, IQR, and standard deviation, s, for the sample. Then IQR s ? 1.3. D) Construct a histogram or stem-and-leaf display. The shape of the graph should be uniform (evenly distributed). 168) Which one of the following suggests that the data set is approximately normal? A) A data set with Q 1 = 14, Q 5 = 68, and s = 41. B) A data set with Q 1 = 1330, Q 3 = 2940, and s = 2440. C) A data set with Q 1 = 105, Q 3 = 270, and s = 33. D) A data set with Q 1 = 2.2, Q 3 = 7.3, and s = 2.1. 22169) Which one of the following suggests that the data set is not approximately normal? A) B) A data set with 68% of the measurements within x ± 2s. C) A data set with IQR = 752 and s = 574. D) Stem Leaves 3 0 3 9 4 2 4 7 7 5 1 3 4 8 8 9 9 9 6 0 0 5 6 6 7 8 7 1 1 5 8 2 7 170) If a population data set is normally distributed, what is the proportion of measurements you would expect to fall within µ ± ?? A) 50% B) 100% C) 68% D) 95% Answer the question True or False. 171) A straight-line shown by a normal probability plot indicates that the data are approximately normally distributed. Solve the problem. 172) Suppose that 40% of the soda-drinking population favors soda A over soda B. Also, suppose you have randomly and independently sampled n = 184 soda drinkers. If asked to approximate the probability of more than half preferring soda A over soda B, you would use the _________ random variable. A) hypergeometric B) uniform C) Poisson D) normal 173) Transportation officials tells us that 80% of the population wear their seat belts while driving. A random sample of 700 drivers has been taken. Find the approximate probability that more than 576 were wearing their seat belts. A) 0.8 B) 0.2 C) 0.0594 D) 0.9406 174) Transportation officials tells us that 80% of the population wear their seat belts while driving. A random sample of 850 drivers has been taken. What is the probability that of seeing 633 individuals or less with their seat belts on? A) approximately 1 B) 0.2 C) 0.8 D) approximately 0 23175) Transportation officials tells us that 60% of the population wear their seat belts while driving. A random sample of 900 drivers has been taken. What is the probability that between 509 and 521 of the drivers were wearing their seat belts? A) 0.8959 B) 0.0160 C) 0.1041 D) 0.0881 176) A certain baseball player hits a home run in 6% of his at-bats. Consider his at-bats as independent events. Suppose we randomly sample n = 750 at-bats of the baseball player. How many home runs do we expect the baseball player to hit in the 750 at-bats? A) 45 B) 42.3 C) 756 D) 6 177) A certain baseball player hits a home run in 8% of his at-bats. Consider his at-bats as independent events. Suppose we randomly sample n = 850 at-bats of the baseball player. Find the probability that this baseball player hits fewer than 52 home runs in the 850 at-bats? A) 0.08 B) 0.92 C) 0.0250 D) 0.9750 178) A certain baseball player hits a home run in 7% of his at-bats. Consider his at-bats as independent events. Suppose we randomly sample n = 800 at-bats of the baseball player. Find the probability that this baseball player hits more than 42 home runs in the 800 at-bats? A) 0.0307 B) 0.9693 C) 0.93 D) 0.07 179) Recent market research reveals that an estimated 36% of U.S. households own one or more personal computers (PC's). Suppose that in a sample of 90 households in a large high-tech community, 14 own PC's. What is the approximate probability that fewer than 14 of the homes sampled would have PC's? A) 0.36 B) approximately 0 C) approximately 1 D) 0.64 180) Recent market research reveals that an estimated 30% of U.S. households own one or more personal computers (PC's). Suppose that we take a sample of 60 households in a large high-tech community. How many of the 60 households do we expect to own PC's? A) 30 B) 18 C) 12.6 D) 90 181) Recent market research reveals that an estimated 36% of U.S. households own one or more personal computers (PC's). Suppose that we take a sample of 140 households in a large high-tech community. What distribution is appropriate to use to estimate the random variable x = the number of the 140 homes that own PC's? A) uniform B) hypergeometric C) Poisson D) normal 182) It is against the law to discriminate against job applicants because of race, religion, sex, or age. Of the individuals who apply for an accountant's position in a large corporation, 41% are over 45 years of age. If the company decides to choose 96 of a very large number of applicants for closer credential screening, claiming that the selection will be random and not age-biased, what is the z-value associated with fewer than 46 of those chosen being over 45 years of age? (Assume that the applicant pool is large enough so that x, the number in the sample over 45 years of age, has a binomial probability distribution.) 183) A loan officer in a large bank has been assigned to screen 69 loan applications during the next week. If her past record indicates that she turns down 18% of the applicants, what is the z-value associated with 64 or more of the 69 applications will be rejected? 184) For the following conditions, determine if it is appropriate to use the normal distribution to approximate a binomial distribution with n = 7 and p = 0.4. 24185) For the following conditions, determine if it is appropriate to use the normal distribution to approximate a binomial distribution with n = 27 and p = 0.5. Answer the question True or False. 186) The binomial distribution can be approximated with the normal distribution if n is large, p is small, and np < 7. 187) The continuity correction factor is the name given to the .5 adjustment necessary when estimating the binomial with the normal distribution. Solve the problem. 188) The lifetime of a new computer follows an exponential distribution with a mean of 6300 hours of use. Find the probability that a randomly selected computer will last more than 12,600 hours. A) .606531 B) .135335 C) .864665 D) .393469 189) The lifetime of a new computer follows an exponential distribution with a mean of 6100 hours of use. Find the probability that a randomly selected computer will last between 1220 hours and 2440 hours. A) .148411 B) .891311 C) .851589 D) .449329 190) The time between landings of airplanes at a certain airport follows an exponential distribution with a mean of 67 seconds. Find the probability that there will be less than a 3 minute gap between landings at this airport. A) 0.068114 B) 0.956212 C) 0.931886 D) 0.043788 191) The time between landings of airplanes at a certain airport follows an exponential distribution with a mean of 39 seconds. Find the probability that gap between landings at this airport will be between 16 seconds and 49 seconds. A) 0.378806 B) 1.000000 C) 0.621194 D) 0.000000 192) The length of time between arrivals of commercial airplanes at a certain airport follows an exponential distribution with a mean of 45 seconds. Assume a commercial airplane just arrived. Find the probability that the next commercial airplane lands in the next 1.6 to 3.9 minutes. A) 0.118442 B) 0.887075 C) 0.005517 D) 0.112925 193) The length of time between arrivals of commercial airplanes at a certain airport follows an exponential distribution with a mean of 45 seconds. Assume a commercial airplane just arrived. Find the probability that the next commercial airplane won't arrive for at least 2.2 minutes. A) 0.946781 B) 0.053219 C) 1.000000 D) 1.564972e-15 194) The time between landings of airplanes at a certain airport follows an exponential distribution with a mean of 64 seconds. Find the probability that there will be at least a 2 minute gap between landings at this airport. A) 0.031743 B) 0.968257 C) 0.153355 D) 0.846645 195) The amount of time between births at the maternity wing of a certain hospital follows an exponential distribution with a mean of 14 minutes. Suppose a birth just took place and that there is only one doctor available to deliver babies at this particular time. Find the probability that the doctor will be able to have at least a 26 minute break before delivering the next baby. A) 0.583645 B) 0.000001 C) 0.156118 D) 0.843882 25196) The amount of time between births at the maternity wing of a certain hospital follows an exponential distribution with a mean of 28 minutes. Suppose a birth just took place. Find the probability that the next birth will not occur for at least 28 minutes. A) .367879 B) .632121 C) .864665 D) .135335 197) The lifetime of a new brand of light bulb follows an exponential distribution with a mean of 1500 hours of use. Find the probability that a randomly selected light bulb will last at least 1500 hours. A) .367879 B) .867879 C) .132121 D) .632121 198) The lifetime of a new brand of light bulb follows an exponential distribution with a mean of 2200 hours of use. Find the probability that a randomly selected light bulb will last between 2000 and 2700 hours. A) 0.109799 B) 0.000000 C) 1.000000 D) 0.890201 199) A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers are willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3.8 minutes. What is the probability a caller put on hold longer than 3.8 minutes will still be there? A) .50 B) 632121 C) .367879 D) .060810 200) A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers are willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3.1 minutes. What is the probability that a randomly selected caller who is placed on hold fewer than 6.4 minutes will still there to place an order? A) 0.126880 B) 0.873120 C) 0.998338 D) 0.001662 201) A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers are willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3.4 minutes. Find the probability a randomly selected caller who is placed on hold more than 6.0 minutes will still be there to place an order? A) 0.997521 B) 0.171237 C) 0.002479 D) 0.828763 202) Suppose x has an exponential distribution with ? = 1.4. Find the following probability: P(x > 2.4). A) 0.180092 B) 0.558035 C) 0.441965 D) 0.819908 203) Suppose x has an exponential distribution with ? = 1.7. Find the following probability: P(x ? 2.1). A) 0.709251 B) 0.290749 C) 0.554930 D) 0.445070 204) The lifetime of a new computer follows an exponential distribution with a mean of 5400 hours of use. Find the probability that a randomly selected computer will last more than 3240 hours. 205) The shelf life of a perishable product is a random variable that is related to consumer acceptance and, ultimately, to sales and profit. Suppose the shelf life of bread is best approximated by an exponential distribution with mean equal to 3 days. What fraction of the loaves stocked today will still be fresh after 6 days on the shelf? 206) The shelf life of a perishable product is a random variable that is related to consumer acceptance and, ultimately, to sales and profit. Suppose the shelf life of bread is best approximated by an exponential distribution with mean equal to 5 days. What proportion of the loaves have a shelf life that is less than 15 days? 26207) The lifetime of a new brand of light bulb follows an exponential distribution with a mean of 2400 hours of use. Find the probability that a randomly selected light bulb lasts less than 3000 hours? Find the mean and standard deviation of the specified probability density function. 208) f(x) = .2e -.2x for [0, ?) A) µ = 6, ? = 6 B) µ = 0.5, ? = 0.6 C) µ = 5, ? = 5 D) µ = 0.5, ? = 0.5 Solve the problem. 209) Which of the following is not one of the properties of the sampling distribution of the sample mean? A) The mean of the sampling distribution is equal to the population mean B) The shape of the sampling distribution is approximately normal if the sample size is sufficiently large (e.g. at least 30). C) The standard deviation of the sampling distribution is equal to the standard deviation of the population divided by the square root of n. D) All of the above are properties of the sampling distribution of the sample mean. 210) If we repeatedly sample from a population samples of size n, and calculate the sample median for each sample, the accumulation of these sample medians would result in __________. A) an estimate of the sample median B) a confidence interval for the population variation C) the sampling distribution of the sample median D) the sampling distribution for the population mean 211) Suppose that repeated samples were selected from a population and the sample variance was calculated for each. The distribution of these sample variances would be called the __________. A) sampling distribution of s 2 B) mean of the sampling distribution C) sampling distribution of x D) standard error 212) The probability distribution shown below describes a population of measurements that can assume values of 1, 6, 11, and 16, each of which occurs with the same frequency: x 1 6 11 16 p(x) 1 4 1 4 1 4 1 4 Taking samples of n = 2 measurements, construct the probability histogram for the sampling distribution of x. 213) The probability distribution shown below describes a population of measurements that can assume values of 5, 10, 15, and 20, each of which occurs with the same frequency: x 5 10 15 20 p(x) 1 4 1 4 1 4 1 4 Find E(x) = µ. Then taking samples of n = 2 measurements, find the expected value, E(x), of x. 27214) The Central Limit Theorem says the sampling distribution of the sample mean is approximately normal under certain conditions. Which of the following is a necessary condition for the Central Limit Theorem to be used? A) The population size must be large (e.g., at least 30). B) The sample size must be large (e.g., at least 30). C) The population from which we are sampling must be normally distributed. D) The population from which we are sampling must not be normally distributed. 215) The Central Limit Theorem is important in statistics because _____. A) for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size B) for any size sample, it says the sampling distribution of the sample mean is approximately normal C) for a large n, it says the population is approximately normal D) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the population 216) Which of the following statements about the sampling distribution of the sample mean is incorrect? A) the sampling distribution is approximately normal whenever the sample size is sufficiently large (n ? 30). B) The sampling distribution is generated by repeatedly taking samples of size n and computing the sample means. C) The mean of the sampling distribution is µ. D) The standard deviation of the sampling distribution is ?. Answer the question True or False. 217) As the sample size taken gets larger, the standard error of the sampling distribution of the sample mean gets larger as well. 218) The Central Limit Theorem guarantees that the population is normal whenever n is sufficiently large. 219) The standard error of the sampling distribution of the sample mean is equal to ?, the standard deviation of the population. Solve the problem. 220) Which piece of information listed below does the Central Limit Theorem allow us to disregard when working with the sampling distribution of the sample mean? A) The shape of the population. B) All can be disregarded when the Central Limit Theorem is used. C) The standard deviation of the population. D) The mean of the population. 221) The Central Limit Theorem is considered powerful in statistics because __________. A) It works for any population distribution provided the sample size is sufficiently large B) It works for any sample size provided the population is normal C) It works for any sample provided the population distribution is known D) It works for any population distribution provided the population mean is known 222) The amount of corn chips dispensed into a 10-ounce bag by the dispensing machine has been identified at possessing a normal distribution with a mean of 10.5 ounces and a standard deviation of .2 ounces. Suppose 100 bags of chips were randomly selected from this dispensing machine. Find the probability that the sample mean weight of these 100 bags exceeded 10.45 ounces. 28223) The amount of money collected by the snack bar at a large university has been recorded daily for the past five years. Records indicate that the mean daily amount collected is $3100 and the standard deviation is $350. The distribution is skewed to the right due to several high volume days (football game days). Suppose that 100 days were randomly selected from the five years and the average amount collected from those days was recorded. Which of the following describes the sampling distribution of the sample mean? A) skewed to the right with a mean of $3100 and a standard deviation of $350 B) normally distributed with a mean of $3100 and a standard deviation of $350 C) normally distributed with a mean of $310 and a standard deviation of $35 D) normally distributed with a mean of $3100 and a standard deviation of $35 224) The amount of corn chips dispensed into a 15-ounce bag by the dispensing machine has been identified at possessing a normal distribution with a mean of 15.5 ounces and a standard deviation of 0.3 ounce. Suppose 100 bags of chips were randomly selected from this dispensing machine. Find the probability that the sample mean weight of these 100 bags exceeded 15.6 ounces. A) .3085 B) .1915 C) approximately 0 D) .6915 225) Suppose Stat I students' ages follow a skewed right distribution with a mean of 24 years old and a standard deviation of 2 years old. If we randomly sampled 150 students, which of the following statements about the sampling distribution of the sample mean age is incorrect? A) The mean of the sampling distribution is approximately 24 years old. B) The standard deviation of the sampling distribution is equal to 2 years old. C) The shape of the sampling distribution is approximately normal. D) All of the above statements are correct. 226) The amount of soda a dispensing machine pours into a 24-ounce can of soda follows a normal distribution with a mean of 24.03 ounces and a standard deviation of 0.03 ounces. Suppose the quality control department at the soda plant sampled 100 sodas and found the average amount of soda in the cans was 24 ounces of soda. Which of the following should the quality control department recommend to the management of the plant? A) The machine should continue to operate as this mean is expected given the dispensing machine's specifications. B) The dispensing machine should be stopped and checked because the results of this sample indicate the machine specifications are not correct. C) Neither of these recommendations is appropriate as this sample information tell us nothing concerning the population specifications of the dispensing machine. 227) The number of red lights run in a day, at a given intersection, possesses a distribution with a mean of 2.6 crimes per day and a standard deviation of 6 red lights run per day. A random sample of 100 days was observed, and the sample mean number of red lights run was calculated. Describe the sampling distribution of the sample mean. A) shape unknown with mean = 2.6 and standard deviation = 0.6 B) approximately normal with mean = 2.6 and standard deviation = 0.6 C) shape unknown with mean = 2.6 and standard deviation = 6 D) approximately normal with mean = 2.6 and standard deviation = 6 228) The average score of all golfers for a particular course has a mean of 77 and a standard deviation of 3. Suppose 36 golfers played the course today. Find the probability that the average score of the 36 golfers exceeded 78. A) .0228 B) .3707 C) .4772 D) .1293 229) The amount of time it takes a student to walk from her home to class has a skewed right distribution with a mean of 10 minutes and a standard deviation of 2.1 minutes. If data were collected from 40 randomly selected walks, describe the sampling distribution of x, the sample mean time. 29230) One year, professional sports players salaries averaged $1.7 million with a standard deviation of $0.6 million. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players exceeded $1.1 million. A) approximately 0 B) .7357 C) approximately 1 D) .2357 231) A random sample of size n is to be drawn from a population with µ = 1300 and ? = 100. What size sample would be necessary in order to reduce the standard error to 10? 232) Find z ?/2 for ? = 0.01. A) 2.33 B) 1.96 C) 2.575 D) 1.645 The filling machine at a bottling plant is operating correctly when the variance of the fill amount is equal to 0.3 ounces. Assume that the fill amounts follow a normal distribution. 233) What is the probability that for a sample of 30 bottles, the sample variance is greater than 0.5? 234) The probability is 0.10 that for a sample of 30 bottles, the sample variance is less than what number? A sample of 25 bottles is taken from the production line at a local bottling plant. Assume that the fill amounts follow a normal distribution. 235) What is the probability that the sample standard deviation is more than 70% of the population standard deviation? 236) The probability is 90% that the sample variance is less than what percent of the population variance? 237) The volume of a one-pound bag of coffee is normally distributed. Suppose you take a random sample of 15 one-pound bags of coffee. Find two values K L and K U such that the probability is 95% that the ratio of the sample standard deviation divided by the population standard deviation is between K L and K U . Solve the problem. 238) What is the confidence level of the following confidence interval for µ? x ± 1.282 ? n A) 78% B) 128% C) 90% D) 95% 239) The registrar's office at State University would like to estimate the average commute time and determine a 95% confidence interval for the average commute time of evening university students from their usual starting point to campus. A member of the staff randomly chooses a parking lot and selects the first 100 evening students who park in the chosen lot starting at 5:00 p.m. The confidence interval is A) not meaningful because the sampling distribution of the sample mean is not normal. B) meaningful because the sample is representative of the population. C) meaningful because the sample size exceeds 30 and the central limit theorem ensures normality of the sampling distribution of the sample mean. D) not meaningful because of the lack of random sampling. 30240) A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.5%, 5.2%). What is the point estimator of the mean percentage of reservations that are canceled on the day of the flight? A) 3.7% B) 3.35% C) 2.60% D) 1.85% 241) Suppose a 95% confidence interval for µ turns out to be (190, 260). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width? A) Increase the sample size. B) Increase the sample size and decrease the confidence level. C) Decrease the confidence level. D) All of the choices will result in a reduced interval width. 242) Suppose a 90% confidence interval for µ turns out to be (140, 270). Based on the interval, do you believe the average is equal to 290? A) Yes, and I am 90% sure of it. B) No, and I am 90% sure of it. C) No, and I am 100% sure of it. D) Yes, and I am 100% sure of it. 243) Forty-five CEOs from the electronics industry were randomly sampled and a 95% confidence interval for the average salary of all electronics CEOs was constructed. The interval was ($100,621, $118,255). At what level of reliability are the inferences derived from this information valid? A) 0.95% B) 47.5% C) 95% D) 5% 244) Forty-five CEOs from the electronics industry were randomly sampled and a 95% confidence interval for the average salary of all electronics CEOs was constructed. The interval was ($112,823, $130,508). Give a practical interpretation of the interval above. A) 95% of the electronics industry CEOs have salaries that fall between $112,823 to $130,508. B) We are 95% confident that the mean salary of all the electronics industry CEOs fall in the interval $112,823 to $130,508. C) 95% of the sampled CEOs salaries fell in the interval $112,823 to $130,508. D) We are 95% confident that the mean salary of the sampled CEOs falls in the interval $112,823 to $130,508. 245) Find the value t 0 such that the following statement is true: P(-t 0 ? t ? t 0 ) = .01 where df = 9. A) 1.833 B) 3.250 C) 2.262 D) 2.2821 246) A marketing research company needs to estimate which of two soft drinks college students prefer. A random sample of n college students produced the following 90% confidence interval for the proportion of college students who prefer drink A: (.313, .553). Identify the point estimate for estimating the true proportion of college students who prefer that drink. A) .12 B) .553 C) .313 D) .433 31247) What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and asked which type of car they drove. A computer package was used to generate the printout below for the proportion of college students who drive American automobiles. SAMPLE PROPORTION = .396 SAMPLE SIZE = 159 UPPER LIMIT = .460 LOWER LIMIT = .332 Which of the following practical interpretations is correct? A) We are 90% confident that the proportion of all college students who drive foreign cars falls between .332 and .460. B) We are 90% confident that the proportion of the 159 sampled students with American cars falls between .332 and .460. C) We are 90% confident that the proportion of all college students who drive American cars falls between .332 and .460. D) 90% of all college students drive American cars between .332 and .460 of the time. 248) We intend to estimate the average driving time of Chicago commuters. From data sampled previously, we believe that the average time is 42 minutes with a standard deviation of 11 minutes. We want our 99 percent confidence interval to have a margin of error of no more than plus or minus 5 minutes. How large a sample do we need? A) 161 B) 6 C) 33 D) 3 249) A local men's clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will randomly sample among its 100,000 items in order to determine the proportion of merchandise that is outdated. The current owners have never determined their outdated percentage and can not help the buyers. Approximately how large a sample do the buyers need in order to insure that they are 98% confident that the margin of error is within 3%? A) 6033 B) 3017 C) 648 D) 1509 250) A math department needs to estimate the average time it takes Statistics I students to finish a computer project to within 2 hours at 98% reliability. It is estimated that the standard deviation of the times is 14 hours. How large a sample should be taken to get the desired interval? A) 267 B) 20 C) 115 D) 17 251) A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following confidence interval: (.438, .642). Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within 1% using 99% reliability? A) 16,471 B) 16,577 C) 15,914 D) 17,240 252) Sales of a new line of athletic footwear are crucial to the success of a newly formed company. The company wishes to estimate the average weekly sales of the new footwear to within $300 with 99% reliability. The initial sales indicate the standard deviation of the weekly sales figures to be approximately $1100. How many weeks of data must be sampled for the company to get the information it desires? A) 26,744 weeks B) 90 weeks C) 35 weeks D) 10 weeks 32253) As an aid in the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, x = 19.8 and s 2 = 25. If the director wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 95% reliability, what size sample should she choose? A) 97 B) 2401 C) 1225 D) 49 254) Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A previous random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. How many citizens would need to be sampled if a 98% confidence interval was desired to estimate the true proportion to within 1%? A) 13,573 B) 13,361 C) 14,116 D) 12,487 255) A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 95% reliability, how many students would need to be sampled? A) 1033 B) 527 C) 250 D) 31 256) A local men's clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will randomly sample among its 100,000 items in order to determine the proportion of merchandise that is outdated. The current owners have never determined their outdated percentage and can not help the buyers. Approximately how large a sample do the buyers need in order to insure that they are 99% confident that the margin of error is within 3%? 257) Suppose you wanted to estimate a binomial proportion, p, correct to within .01 with probability 0.98. What size sample would need to be selected if p is known to be approximately 0.75? 258) A marketing research company needs to estimate a population mean to within 48 units with 95% reliability. The population standard deviation is estimated to be 280 units. What size sample should be selected? 259) Sales of a new line of athletic footwear are crucial to the success of a newly formed company. The company wishes to estimate the average weekly sales of the new footwear to within $300 with 99% reliability. The initial sales indicate the standard deviation of the weekly sales figures to be approximately $1675. How many weeks of data must be sampled for the company to get the information it desires? 260) A university is considering a change in the way students pay for their education. Presently, the students pay $16 per credit hour. The university is contemplating charging each student a set fee of $240 per quarter, regardless of how many credit hours each takes. To see if this proposal would be economically feasible, the university would like to know how many credit hours, on the average, each student takes per quarter. A random sample of 250 students yields a mean of 14.1 credit hours per quarter and a standard deviation of 2.4 credit hours per quarter. Suppose the administration wanted to estimate the mean to within 0.1 credit hours at 98% reliability. How large a sample would they need to take? 261) In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a __________ interval. A) less significant B) narrower C) biased D) wider Answer the question True or False. 262) One way of reducing the width of a confidence interval is to reduce the size of the sample taken. 33263) If no estimate of P exists when determining the sample size, we can use .5 in the formula to get a value for n. Solve the problem. 264) What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and asked which type of car they drove. A computer package was used to generate the printout below of a 90% confidence interval for the proportion of college students who drive American automobiles. SAMPLE PROPORTION = .396 SAMPLE SIZE = 159 UPPER LIMIT = .460 LOWER LIMIT = .332 Based on the interval above, do you believe that 21% of all college students drive American automobiles? A) Yes, and we are 90% confident of it. B) Yes, and we are 100 %sure of it. C) No, and we are 90% confident of it. D) No, and we are 100% sure of it. 265) An article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 535 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 90% confidence level. A) .37 ± .034 B) .37 ± .001 C) .63 ± .001 D) .63 ± .034 266) An article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 549 teenagers. Using 99% reliability, can we say that more than .418 of all teenagers want to discuss school with their parents? A) Yes, since the value falls inside the 99% confidence interval. B) No, since the value is not contained in the 99% confidence interval. C) No, since the value falls inside the 99% confidence interval. D) Yes, since the value is not contained in the 99% confidence interval. 267) Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4,000 citizens yielded 2250 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation. A) .4375 B) 4000 C) .5625 D) 2250 268) Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4,000 citizens yielded 2,250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval. A) .4375 ± .0129 B) .4375 ± .4048 C) .5625 ± .4048 D) .5625 ± .0129 34269) A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 95% confidence interval to estimate the true proportion of students on financial aid. A) .59 ± .068 B) .59 ± .005 C) .59 ± .474 D) .59 ± .002 270) A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. The 95% confidence interval for p is 59 ± .07. Interpret this interval. A) 95% of the students get between 52% and 66% of their tuition paid for by financial aid. B) We are 95% confident that the true proportion of all students receiving financial aid is between .52 and .66. C) We are 95% confident that between 52% and 66% of the sampled students receive some sort of financial aid. D) We are 95% confident that 59% of the students are on some sort of financial aid. 271) A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 98% confidence interval: (.438, .642). State the level of reliability used to create the confidence interval. A) 64.2% B) between 43.8% and 64.2% C) 72% D) 98% 272) A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% confidence interval: (.438, .642). Based on the interval above, is the population proportion of females equal to 45%? A) No, and we are 90% sure of it. B) Maybe. 45% is a believable value of the population proportion based on the information above. C) No, the proportion is 54%. D) Yes, and we are 90% sure of it. 273) The U.S. Commission on Crime wishes to estimate the fraction of crimes related to firearms in an area with one of the highest crime rates in the country. The commission randomly selects 600 files of recently committed crimes in the area and finds 380 in which a firearm was reportedly used. Find a 95% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used. 274) An article in a Florida newspaper reports on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 505 teenagers. Estimate the proportion of all teenagers who want more family discussions about religion. Use a 90% confidence level. 275) A marketing research company needs to estimate which of two soft drinks college students prefer. A random sample of n college students produced the following 95% confidence interval for the proportion of college students who prefer drink A: (.344, .494). A friend suggests that the proportion of all students who prefer that drink is 29%. Comment on your friend's suggestion. A) Based on this information, all you can say is that the proportion may be 29%. B) Your friend is wrong, and you are 95% certain. C) Your friend is right, and you are 100% certain of it. D) Your friend is correct, and you are 95% certain. 35276) A marketing research company needs to estimate which of two soft drinks college students prefer. A random sample of 329 college students produced the following 95% confidence interval for the proportion of college students who prefer one of the colas: (.329, .465). What assumptions are necessary for any inferences derived from this printout to be valid? A) No assumptions are necessary. B) The population proportion has an approximately normal distribution. C) The sample was randomly selected from an approximately normal population. D) The sample proportion equals the population proportion. 277) What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and asked which type of car they drove. A computer package was used to generate the printout below for the proportion of college students who drive American automobiles. SAMPLE PROPORTION = .380497 SAMPLE SIZE = 159 UPPER LIMIT = .464240 LOWER LIMIT = .331153 What proportion of the sampled students drive foreign automobiles? A) .464240 B) .380497 C) .331153 D) .619503 278) Find the value t 0 such that the following statement is true: P(-t 0 ? t ? t 0 ) = .05 where df = 15. A) 2.602 B) 2.131 C) 2.947 D) 1.753 279) Find the value t 0 such that the following statement is true: P(-t 0 ? t ? t 0 ) = .10 where df = 14. A) 1.345 B) 2.624 C) 2.145 D) 1.761 280) Let t 0 be a specific values of t. Find t 0 such that the following statement is true: P(t ? t 0 ) = .1 where df = 20 A) 1.325 B)-1.325 C)-1.328 D) 1.328 281) You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years of ownership. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 90% confidence interval. You manage to obtain data on 17 recently resold 5 year old foreign sedans of that model. These 17 cars were resold at an average price of $12,690 with a standard deviation of $700. What is the correct form of a 90% confidence interval for the true mean resale value of a 5 year old specific foreign sedan? A) 12,690 ± 1.74(700/ 17) B) 12,690 ± 1.746(700/ 16) C) 12,690 ± 1.746(700/ 17) D) 12,690 ± 1.645(700/ 17) 36282) You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years of ownership. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 99% confidence interval. You manage to obtain data on 17 recently resold 5 year old foreign sedans of that model. These 17 cars were resold at an average price of $12,460 with a standard deviation of $800. Suppose that the interval is calculated to be ($11,893.24, $13,026.76). How could we alter the sample size and the confidence coefficient in order to guarantee a decrease in the width of the interval? A) Increase the sample size but decrease the confidence coefficient. B) Decrease the sample size but increase the confidence coefficient. C) Keep the sample size the same but increase the confidence coefficient. D) Increase the sample size and increase the confidence coefficient. 283) How much money does the average professional football fan spend on food at a single football game? That question was posed to 10 randomly selected football fans. The sampled results show that sample mean and standard deviation were $18.00 and $3.30, respectively. Use this information to create a 90% confidence interval for the mean. A) 18 ± 1.822(3.30/ 10) B) 18 ± 1.383(3.30/ 10) C) 18 ± 1.796(3.30/ 10) D) 18 ± 1.812(3.30/ 10) 284) A marketing research company needs to estimate the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 90% confidence interval was calculated to be ($2,181,260, $5,836,180). Explain what the phrase "90% confident" means. A) The probability that the population mean falls in any confidence interval constructed is .90. B) In repeated sampling, 90% of the intervals constructed would contain µ. C) 90% of the population values will fall in the interval. D) 90% of the similarly constructed intervals would contain the value of the sample mean. 285) A marketing research company needs to estimate the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260, $5,836,180). What assumptions are necessary for this confidence interval to be valid? A) None. The Central Limit Theorem applies. B) The total compensation of CEOs in the service industry is approximately normally distributed. C) The sample is randomly selected from a population of total compensations that is a t distribution. D) The distribution of the means is approximately normal. 286) A marketing research company needs to estimate the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 97% confidence interval was calculated to be ($2,181,260, $5,836,180). Based on the interval above, do you believe the average total compensation of CEOs in the service industry is more than $3,000,000? A) Yes, and I am 78% confident of it. B) Yes, and I am 97% confident of it. C) I am 97% confident that the average compensation is $3,000,000. D) I cannot conclude that the average exceeds $3,000,000 at the 97% confidence level. 287) A marketing research company needs to estimate the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 99% confidence interval was calculated to be ($2,181,260, $5,836,180). What would happen to the confidence interval above if the confidence level were changed to 98%? A) There would be no change in the interval width. B) The interval would get wider. C) The interval width would get narrower. D) It is impossible to tell until the 98% interval is constructed. 37288) Suppose a 98% confidence interval for µ turns out to be (1,000, 2,100). If this interval was based on a sample of size n = 20, explain what assumptions are necessary for this interval to be valid. A) The population of salaries must have an approximate t distribution. B) The sampling distribution of the sample mean must have a normal distribution. C) The sampling distribution must be biased with 19 degrees of freedom. D) The population must have an approximately normal distribution. 289) A computer package was used to generate the following printout for estimating the sale price of homes in a particular neighborhood. X = sale_price SAMPLE MEAN OF X = 46,600 SAMPLE STANDARD DEV = 13,747 ` SAMPLE SIZE OF X = 15 CONFIDENCE = 90 UPPER LIMIT = 52,850.6 SAMPLE MEAN OF X = 46,600 LOWER LIMIT = 40,349.4 At what level of reliability is the confidence interval made? A) 45% B) 90% C) 10% D) 55% 290) A computer package was used to generate the following printout for estimating the sale price of homes in a particular neighborhood. X = sale_price SAMPLE MEAN OF X = 46,600 SAMPLE STANDARD DEV = 13,747 SAMPLE SIZE OF X = 15 CONFIDENCE = 98 UPPER LIMIT = 55,913.8 SAMPLE MEAN OF X = 46,600 LOWER LIMIT = 37,286.2 Which of the following is a practical interpretation of the interval above? A) We are 98% confident that the true sale price of all homes in this neighborhood fall between $37,286.20 and $55,913.80. B) 98% of the homes in this neighborhood have sale prices that fall between $37,286.20 and $55,913.80. C) We are 98% confident that the mean sale price of all homes in this neighborhood fall between $37,286.20 and $55,913.80. D) All are correct practical interpretations of this interval. 38291) A computer package was used to generate the following printout for estimating the sale price of homes in a particular neighborhood. X = sale_price SAMPLE MEAN OF X = 46,500 SAMPLE STANDARD DEV = 13,747 SAMPLE SIZE OF X = 15 CONFIDENCE = 90 UPPER LIMIT = 52,750.60 SAMPLE MEAN OF X = 46,500 LOWER LIMIT = 40,249.40 What assumptions are necessary for any inferences derived from this printout to be valid? A) The sample was randomly selected from an approximately normal population. B) The population mean has an approximate normal distribution. C) The sample variance equals the population variance. D) All of the above are necessary. 292) A computer package was used to generate the following printout for estimating the sale price of homes in a particular neighborhood. X = sale_price SAMPLE MEAN OF X = 46,600 SAMPLE STANDARD DEV = 13,747 SAMPLE SIZE OF X = 15 CONFIDENCE = 98 UPPER LIMIT = 55,913.80 SAMPLE MEAN OF X = 46,600 LOWER LIMIT = 37,286.20 A friend suggests that the mean sale price of homes in this neighborhood is $50,000. Comment on your friend's suggestion. A) Your friend is correct, and you are 100% certain. B) Your friend is correct, and you are 98% certain. C) Your friend is wrong, and you are 98% certain. D) Based on this printout, all you can say is that the mean sale price might be $50,000. 293) To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette gave a mean nicotine content of 26.9 milligrams and standard deviation of 2.5 milligrams for a sample of n = 9 cigarettes. Construct a 90% confidence interval for the mean nicotine content of this brand of cigarette. A) 26.9 ± 1.620 B) 26.9 ± 1.550 C) 26.9 ± 1.644 D) 26.9 ± 1.528 39294) To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette gave a mean nicotine content of 27.2 milligrams and standard deviation of 2.1 milligrams for a sample of n = 9 cigarettes. The FDA claims that the mean nicotine content exceeds 30.2 milligrams for this brand of cigarette, and their stated reliability is 98%. Do you agree? A) Yes, since the value 30.2 does not fall in the 98% confidence interval. B) No, since the value 30.2 does not fall in the 98% confidence interval. C) Yes, since the value 30.2 does fall in the 98% confidence interval. D) No, since the value 30.2 does fall in the 98% confidence interval. 295) Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of eight private colleges in the United States revealed the following endowments (in millions of dollars): 85.7, 45.7, 240.8, 485.7, 126.7, 166.1, 104.7, and 216. What value will be used as the point estimate for the mean endowment of all private colleges in the United States? A) 210.2 B) 8 C) 183.925 D) 1471.4 296) Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of eight private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. Summary statistics yield x = 180.975 and s = 143.042. Calculate a 90% confidence interval for the mean endowment of all private colleges in the United States. A) 180.975 ± 95.836 B) 180.975 ± 94.066 C) 180.975 ± 100.561 D) 180.975 ± 102.453 297) The increasing cost of health care is an important issue today. Suppose that a random sample of 13 small companies that offer paid health insurance as a benefit was selected. The mean health insurance cost per worker per month was $131, and the standard deviation was $32. What assumptions are necessary for a reliable confidence interval to be constructed? A) None. The Central Limit Theorem takes care of any needed assumptions. B) The sample is approximately normally distributed. C) The sample was randomly selected from a population with an approximate t distribution. D) The sample was randomly selected from a population with an approximately normal distribution. 298) The increasing cost of health care is an important issue today. Suppose that a random sample of 23 small companies that offer paid health insurance as a benefit was selected. The mean health insurance cost per worker per month was $132, and the standard deviation was $32. Calculate a 95% confidence interval for the mean health cost per worker per month for all small companies. A) 132 ± 13.078 B) 132 ± 13.805 C) 132 ± 13.839 D) 132 ± 11.457 299) You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years of ownership. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 95% confidence interval. You manage to obtain data on 17 recently resold 5 year old foreign sedans of that model. These 17 cars were resold at an average price of $13,800 with a standard deviation of $800. Create a 95% confidence interval for the true mean resale value of a 5 year old foreign sedan of that model. 300) A marketing research company needs to estimate the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 97% confidence interval was calculated to be ($2,181,260, $5,836,180). Give a practical interpretation of the confidence interval. 40301) A marketing research company needs to estimate the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 97% confidence interval was calculated to be ($2,181,260, $5,836,180). Based on the interval above, do you believe the average total compensation of CEOs in the service industry is more than $1,500,000? 302) A computer package was used to generate the following printout for estimating the sale price of homes in a particular neighborhood. X = sale_price SAMPLE MEAN OF X = 46300 SAMPLE STANDARD DEV = 13747 SAMPLE SIZE OF X = 25 CONFIDENCE = 90 UPPER LIMIT = 51003.90 SAMPLE MEAN OF X = 46300 LOWER LIMIT = 41596.10 A friend suggests that the mean sale price of homes in this neighborhood is $45,000. Comment on your friend's suggestion. 303) The increasing cost of health care is an important issue today. Suppose that a random sample of 23 small companies that offer paid health insurance as a benefit was selected. The mean health insurance cost per worker per month was $131, and the standard deviation was $26. Construct a 95% confidence interval for the average health cost per worker per month for all small companies. 304) Forty-five CEOs from the electronics industry were randomly sampled and a 90% confidence interval for the average salary of all electronics CEOs was constructed. The interval was ($149,786, $164,920). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width? A) Decrease the sample size and decrease the confidence level. B) Increase the sample size and decrease the confidence level. C) Increase the sample size and increase the confidence level. D) Decrease the sample size and increase the confidence level. 305) A university is considering a change in the way students pay for their education. Presently, the students pay $16 per credit hour. The university is contemplating charging each student a set fee of $240 per quarter, regardless of how many credit hours each takes. To see if this proposal would be economically feasible, the university would like to know how many credit hours, on the average, each student takes per quarter. A random sample of 250 students yields a mean of 14.1 credit hours per quarter and a standard deviation of 2.3 credit hours per quarter. Estimate the mean credit hours per student per quarter using a 99% confidence interval. A) 14.1 ± .016 B) 14.1 ± .375 C) 14.1 ± .024 D) 14.1 ± .247 41306) A university is considering a change in the way students pay for their education. Presently, the students pay $16 per credit hour. The university is contemplating charging each student a set fee of $240 per quarter, regardless of how many credit hours each takes. To see if this proposal would be economically feasible, the university would like to know how many credit hours, on the average, each student takes per quarter. A random sample of 250 students yields a mean of 15.5 credit hours per quarter and a standard deviation of 1.7 credit hours per quarter. Suppose a 98% confidence interval turned out to be 15.5 ± 0.251. Interpret the interval. A) We are 98% confident that the average credit hours per quarter of the sampled students falls in the interval 15.249 to 15.751 hours. B) 98% of the students take between 15.249 to 15.751 credit hours per quarter. C) The probability that a student takes 15.249 to 15.751 hours in a quarter is 0.98. D) We are 98% confident that the average credit hours per quarter of students at the college falls in the interval 15.249 to 15.751 hours. 307) As an aid in the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 49 different 24-hour periods and determines the number of admissions for each. For this sample, x = 18.5 and s 2 = 25. Which of the following assumptions is necessary in order for a confidence interval to be valid? A) The mean of the sample equals the mean of the population. B) The population sampled from has an approximate t distribution. C) The population sampled from has an approximate normal distribution. D) None of these assumptions are necessary. 308) As an aid in the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 81 different 24-hour periods and determines the number of admissions for each. For this sample, x = 18.2 and s 2 = 25. Estimate the mean number of admissions per 24-hour period with a 95% confidence interval. A) 18.2 ± .121 B) 18.2 ± .528 C) 18.2 ± 1.089 D) 18.2 ± 5.444 309) Suppose a large labor union wishes to estimate the mean number of hours per month a union member is absent from work. The union decides to sample 403 of its members at random and monitor their working time for 1 month. At the end of the month, the total number of hours absent from work is recorded for each employee. If the mean and standard deviation of the sample are x = 8.6 hours and s = 2.6 hours, find a 95% confidence interval for the true mean number of hours absent per month per employee. A) 8.6 ± .123 B) 8.6 ± .157 C) 8.6 ± .254 D) 8.6 ± .013 310) How much money does the average professional football fan spend on food at a single football game? That question was posed to 48 randomly selected football fans. The sampled results show that sample mean and standard deviation were $12.00 and $2.90, respectively. Find and interpret a 99% confidence interval for µ. 311) To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette gave a mean nicotine content of 24.8 milligrams and standard deviation of 2.6 milligrams for a sample of n = 86 cigarettes. Find a 95% confidence interval for µ. 312) Explain what the phrase 95% confident means when we interpret a 95% confidence interval for µ. A) In repeated sampling, 95% of similarly constructed intervals would contain the value of the population mean. B) 95% of the observations in the population fall within the bounds of the calculated interval. C) 95% of similarly constructed intervals would contain the value of the sampled mean. D) The probability that the mean falls in the calculated interval is 0.95. 42313) Suppose a 95% confidence interval for µ turns out to be (1,000, 2,100). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Explain why an increase in sample size will lead to a narrower interval estimate of µ. Answer the question True or False. 314) One way of reducing the width of a confidence interval is to reduce the confidence level. 315) The Central Limit Theorem guarantees an approximately normal sampling distribution for the sample mean for large sample sizes, so no knowledge about the distribution of the population is necessary for this interval to be valid. Solve the problem. 316) What is the Rule of Thumb for the Finite Population Correction Factor? 317) When is the finite population correction factor used? 318) A revenue department is under orders to reduce the time small business owners spend on filling out pension form ABC-5500. Previously the average time spent on the form was 5.1 hours. In order to prove that the time to fill out the form is reduced, a sample of 48 small business owners who annually complete the form is randomly chosen, and their completion times are recorded. The mean completion time for ABC-5500 form was 4.7 hours with a standard deviation of 2.9 hours. In order to prove the time to complete the form is reduced, state the appropriate null and alternative hypotheses to test. A) H 0 : µ = 5.1 H a : µ < 5.1 B) H 0 : µ = 5.1 H a : µ > 5.1 C) H 0 : µ = 5.1 H a : µ = 5.1 D) H 0 : µ > 5.1 H a : µ < 5.1 E) H 0 : µ = 5.1 H a : µ ? 5.1 319) The owner of Get-A-Away Travel has recently surveyed a random sample of 357 customers of the agency. He would like to determine whether or not the mean age of the agency's customers is over 35. If so, he plans to alter the destination of their special cruises and tours. If not, no changes will be made. The appropriate hypotheses are H 0 : µ = 35, H a : µ > 35. If he concludes the mean age is over 35 when it is not, he makes a __________ error. If he concludes the mean age is not over 35 when it is, he makes a __________ error. A) Type I; Type I B) Type II; Type I C) Type II; Type II D) Type I; Type II 320) An insurance company states that their claim office is able to process all death claims within 4 working days. Recently there have been several complaints that it took longer than 4 days to process a claim. Top management wants to make sure that the situation is status quo and sets up a statistical test with a null hypothesis that the average time for processing a claim is 4 days, and an alternative hypothesis that the average time for processing a claim is greater than 4 days. After completing the statistical test, it is concluded that the average exceeds 4 days. However, it is eventually learned that the mean process time is really 4 days. What type of error occurred in the statistical test? A) Type II error B) Type III error C) No error occurred in the statistical sense. D) Type I error 321) Suppose we wish to test H 0 : µ = 53 vs. H a : µ > 53. What will result if we conclude that the mean is greater than 53 when its true value is really 58? A) We have made a correct decision. B) We have made a Type I error. C) We have made a Type II error. D) None of the above are correct. 43322) How many tissues should a package of tissues contain? Researchers determined that 66 tissues is the average number of tissues used during a cold. Suppose a random sample of 2500 tissue users yielded the following data on the number of tissues used during a cold: x = 59, s = 21. Give the null and alternative hypothesis to determine if the number of tissues used during a cold is less than 66. A) H 0 : µ = 66 vs. H a : µ ? 66 B) H 0 : µ = 66 vs. H a : µ < 66 C) H 0 : µ = 66 vs. H a : µ > 66 D) H 0 : µ > 66 vs. H a : µ ? 66 323) A bottling company needs to produce bottles that will hold 10 ounces of liquid for a local brewery. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 28 bottles and finds the average amount of liquid held by the 28 bottles is 9.5 ounces with a standard deviation of .17 ounces. What is the set of hypotheses the company wishes to test? A) H 0 : µ = 10 vs. H a : µ < 10 B) H 0 : µ = 10 vs. H a : µ > 10 C) H 0 : µ < 10 vs. H a : µ = 10 D) H 0 : µ = 10 vs. H a : µ ? 10 324) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 26 minutes. The owner has randomly selected 17 customers and has delivered pizzas to their homes. What are the hypotheses the owner should test to show that the pizza delivery will not be successful? A) H 0 : µ = 26 vs. H a : µ > 26 B) H 0 : µ = 26 vs. H a : µ ? 26 C) H 0 : µ < 26 vs. H a : µ = 26 D) H 0 : µ = 26 vs. H a : µ < 26 325) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 33 minutes. The owner has randomly selected 23 customers and has delivered pizzas to their homes. The owner of the store views the delivery possibility as a method of expanding her business. She is concerned with the possibility of incorrectly concluding that the mean delivery time exceeds 33 minutes, when, in fact, the mean really equals 33 minutes. In terms of our errors, she is concerned with making _______ error. A) a Type II B) a Type I C) a Type III D) both a Type I and Type II 326) I want to test H 0 : p = .3 vs. H a : p ? .3 using a test of hypothesis. If we concluded that p is .3 when, in fact, the true value of p is not .3, then we have made a: A) Type II error B) Type I and Type II error C) correct decision D) Type I error 327) Researchers have claimed that the average number of headaches during a semester of Statistics is 10. Statistics professors dispute this claim vehemently. Statistic professors believe the average is much more than this. They sample n = 25 students and find the sample mean is 15 and the sample standard deviation is 2. Which of the following represent the null and alternative hypotheses that the professors wish to test? A) H 0 : µ = 10 vs. H a : µ ? 10 B) H 0 : µ < 10 vs. H a : µ = 10 C) H 0 : µ = 10 vs. H a : µ < 10 D) H 0 : µ = 10 vs. H a : µ > 10 44328) A local tennis pro-shop strings tennis rackets at the tension (pounds per square inch) requested by the customer. Recently a customer made a claim that the pro-shop consistently strings rackets at lower tensions, on average, than requested. To support this claim, the customer asked the pro shop to string 11 new rackets at 57 psi. Upon receiving the rackets, the customer measured the tension of each and calculated the following summary statistics: x = 55 psi, s = 3.3 psi. Set up the null and alternative hypotheses for testing the claim. A) H 0 : µ = 57 vs. H a : µ ? 57 B) H 0 : µ = 57 vs. H a :µ < 57 C) H 0 : x = 55 vs. H a : x > 55 D) H 0 : µ = 57 vs. H a :µ > 57 329) A local tennis pro-shop strings tennis rackets at the tension (pounds per square inch) requested by the customer. Recently a customer made a claim that the pro-shop consistently strings rackets at lower tensions, on average, than requested. To support this claim, the customer asked the pro shop to string 10 new rackets at 54 psi. Upon receiving the rackets, the customer measured the tension of each and calculated the following summary statistics: x = 53 psi, s = 3.2 psi. In order to conduct the test, the customer selected a significance level of ? = .05. Interpret this value. A) There is a 5% chance that the sample will be biased. B) The smallest value of ? that you can use and still reject H 0 is .05. C) The probability of making a Type II error is .95. D) The probability of concluding that the true mean is less than 54 psi when in fact it is equal to 54 psi is only .05. 330) A national organization has been working with utilities throughout the nation to find sites for large wind machines for generating electric power. Wind speeds must average more than 15 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted tests at a particular site under construction for a wind machine. Based on a sample of n = 141 wind speed recordings (taken at random intervals) at the site, the wind speeds averaged x = 14.2 mph, with a standard deviation of s = 3.5 mph. To determine whether the site meets the organization's requirements, consider the test, H 0 : µ = 15 vs. H a : µ > 15, where µ is the true mean wind speed at the site and ? = .05. Fill in the blanks. "A Type I error in the context of this problem is to conclude that the true mean wind speed at the site _____ 15 mph when it actually _____ 15 mph." A) equals; equals B) exceeds; exceeds C) exceeds; equals D) equals; exceeds 331) If I specify ß to be equal to .22, then the value of ? must be .78. 332) A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 21% of the women who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 94 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in eleven. Specify the null and alternative hypotheses that the researchers wish to test. 333) According to advertisements, a strain of soybeans planted on soil prepared with a specified fertilizer treatment has a mean yield of 529 bushels per acre. Twenty farmers who belong to a cooperative plant the soybeans. Each uses a 40-acre plot and records the mean yield per acre. The mean and variance for the sample of 20 farms are x = 496 and s 2 = 9240. Specify the null and alternative hypothesis used to determine if the mean yield for the soybeans is different than advertised. 334) What is the probability associated with not making a Type II error? A) (1 - ?) B) ß C) (1 - ß) D) ? 45335) We never conclude "Accept H 0 " in a test of hypothesis. This is because: A) ? is the probability of a Type I error. B) The rejection region is not known. C) ß = p(Type II error) is not known. D) The p-value is not small enough. 336) The value that separates a rejection region from an acceptance region is called a __________. A) parameter B) critical value C) significance level D) confidence coefficient 337) A __________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis. A) critical value B) significance level C) test statistic D) parameter 338) A hypothesis test is used to prevent a machine from underfilling or overfilling quart bottles of beer. On the basis of sample, the null hypothesis is rejected and the machine is shut down for inspection. A thorough examination reveals there is nothing wrong with the filling machine. From a statistical point of view: A) A Type II error was made. B) A correct decision was made. C) A Type I error was made. D) Both Type I and Type II errors were made. Answer the question True or False. 339) We do not accept H 0 because we are concerned with making a Type II error. 340) In a test of hypothesis, the sampling distribution of the test statistic is calculated under the assumption that the alternative hypothesis is true. 341) A Type I error occurs when we accept a false null hypothesis. Solve the problem. 342) A national organization has been working with utilities throughout the nation to find sites for large wind machines for generating electric power. Wind speeds must average more than 16 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted tests at a particular site under construction for a wind machine. Based on a sample of n = 40 wind speed recordings (taken at random intervals) at the site, the wind speeds averaged x = 15.3 mph, with a standard deviation of s = 3.7 mph. To determine whether the site meets the organization's requirements, consider the test, H 0 : µ = 16 vs. H a : µ > 16, where µ is the true mean wind speed at the site and ? = .01. Suppose the value of the test statistic were computed to be -1.20. State the conclusion. A) At ? = .01, there is insufficient evidence to conclude the true mean wind speed at the site exceeds 16 mph. B) We are 99% confident that the site does not meet the organization's requirements. C) We are 99% confident that the site meets the organization's requirements. D) At ? = .01, there is sufficient evidence to conclude the true mean wind speed at the site exceeds 16 mph. 343) How many tissues should a package of tissues contain? Researchers determined that 55 tissues is the average number of tissues used during a cold. Suppose a random sample of 10,000 tissue users yielded the following data on the number of tissues used during a cold: x = 41, s = 21. Using the sample information provided, calculate the value of the test statistic. A) z = 41 - 55 21 10,000 2 B) z = 41 - 55 21 2 10,000 C) z = 41 - 55 21 D) z = 41 - 55 21 10,000 46344) How many tissues should a package of tissues contain? Researchers determined that 47 tissues is the average number of tissues used during a cold. Suppose a random sample of 2500 tissue users yielded the following data on the number of tissues used during a cold: x = 35, s = 15. Suppose the alternative we wanted to test was H a : µ < 47. State the correct rejection region for ? = .05. A) Reject H 0 if z > 1.645. B) Reject H 0 if z < -1.645. C) Reject H 0 if z < -1.96. D) Reject H 0 if z > 1.96 or z < -1.96. 345) How many tissues should a package of tissues contain? Researchers determined that 56 tissues is the average number of tissues used during a cold. Suppose a random sample of 10,000 tissue users yielded the following data on the number of tissues used during a cold: x = 46, s = 17. Suppose the test statistic does fall in the rejection region at ? = .05. What is the correct conclusion? A) At ? = .05, accept H 0 . B) At ? = .05, reject H 0 . C) At ? = .05, we fail to reject H 0 . D) At ? = .10, we fail to reject H 0 . 346) We have created a 99% confidence interval for µ with the result (11, 16). What conclusion will we make if we test H 0 : µ = 21 vs. H a : µ ? 21 at ? = .01? A) Fail to reject H 0 . B) Accept H 0 in favor of H a . C) Reject H 0 in favor of H a . D) We cannot tell what our decision will be with the information given. 347) Suppose we wish to test H 0 : µ ? 34 vs. H a : µ < 34 Which of the following possible sample results gives the most evidence to support H a (i.e., reject H 0 )? A) x = 36, s = 2 B) x = 30, s = 5 C) x = 31, s = 5 D) x = 32, s = 3 348) Consider the following printout. HYPOTHESIS: VARIANCE X = x X = gpa SAMPLE MEAN OF X= 1.9931 SAMPLE VARIANCE OF X= .18000 SAMPLE SIZE OF X= 174 HYPOTHESIZED VALUE (x)= 2.1 VARIANCE X - x = -.1069 z = -3.32366 Suppose we tested H a : µ < 2.1. Find the appropriate rejection region if we used an ? = .05. A) Reject if z > 1.96 or z < -1.96. B) Reject if z < -1.96. C) Reject if z > 1.645 or z < -1.645. D) Reject if z < -1.645. 47349) Consider the following printout. HYPOTHESIS: VARIANCE X = x X = gpa SAMPLE MEAN OF X= 3.2854 SAMPLE VARIANCE OF X= .22000 SAMPLE SIZE OF X= 243 HYPOTHESIZED VALUE (x)= 3.4 VARIANCE X - x = -.1146 z = -3.80870 State the proper conclusion when testing H 0 : µ = 3.4 vs. H a : µ < 3.4 at = .05. A) Reject H 0 . B) Accept H 0 . C) Fail to reject H 0 . D) We cannot determine from the information given. 350) Consider the following printout. HYPOTHESIS: VARIANCE X = x X = gpa SAMPLE MEAN OF X= 2.4544 SAMPLE VARIANCE OF X= .24000 SAMPLE SIZE OF X= 224 HYPOTHESIZED VALUE (x)= 2.6 VARIANCE X - x = -.1456 z = -4.44815 Is this a large enough sample for this analysis to work? A) Yes, since the population of GPA scores is approximately normally distributed. B) No. C) Yes, since n = 224, which is 30 or more. D) Yes, since the interval p ± 3 pq/n does not contain 0 or 1. 48351) A national organization has been working with utilities throughout the nation to find sites for large wind machines for generating electric power. Wind speeds must average more than 20 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted tests at a particular site under construction for a wind machine. Based on a sample of n = 43 wind speed recordings (taken at random intervals) at the site, the wind speeds averaged x = 19.2 mph, with a standard deviation of s = 3.8 mph. To determine whether the site meets the organization's requirements, consider the test, H 0 : µ = 20 vs. H a : µ > 20, where µ is the true mean wind speed at the site and ? = .01. Suppose the value of the test statistic were computed to be -1.38. State the conclusion. A) At ? = .01, there is sufficient evidence to conclude the true mean wind speed at the site exceeds 20 mph. B) We are 99% confident that the site does not meet the organization's requirements. C) At ? = .01, there is insufficient evidence to conclude the true mean wind speed at the site exceeds 20 mph. D) We are 99% confident that the site meets the organization's requirements. 352) A revenue department is under orders to reduce the time small business owners spend on filling out pension form ABC-5500. Previously the average time spent on the form was 70 hours. In order to prove that the time to fill out the form is reduced, a sample of 99 small business owners who annually complete the form is randomly chosen and their completion times are recorded. The mean completion time for ABC-5500 form was 69.6 hours with a standard deviation of 29 hours. State the rejection region for the desired test if testing at ? = .10. 353) State University uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 840 hours. A manufacturer claims that its new brands of bulbs, which cost the same as the brand the university currently uses, has a mean life of more than 840 hours. The university has decided to purchase the new brand if, when tested, the test evidence supports the manufacturer's claim at the .01 significance level. Suppose 54 bulbs were tested with the following results: x = 868 hours, s = 85 hours. Find the rejection region for the test of interest to the State University. 354) State University uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 1000 hours. A manufacturer claims that its new brands of bulbs, which cost the same as the brand the university currently uses, has a mean life of more than 1000 hours. The university has decided to purchase the new brand if, when tested, the test evidence supports the manufacturer's claim at the .05 significance level. Suppose 49 bulbs were tested with the following results: x = 1020 hours, s = 70 hours. Conduct the test using ? = .05. 355) A journal article reported that for the 1998-1999 academic year, four-year private colleges charged students an average of $8934 for tuition and fees. Suppose that for 1999-2000 a random sample of 30 private colleges yielded the following data on tuition and fees: x = $9880 and s = $1730. Assume that $8934 is the population mean for 1998-1999. Suppose it is desired to determine if the average for tuition and fees exceeds the reported $8934. The p-value for the test was reported to be p = .0013. State the proper conclusion using an ? = .01. 356) Given H 0 : µ = 25, H a : µ ? 25, and P = 0.041. Do you reject or fail to reject H 0 at the 0.01 level of significance? A) reject H 0 B) fail to reject H 0 C) not sufficient information to decide 357) Given H 0 : µ = 18, H a : µ < 18, and P = 0.085. Do you reject or fail to reject H 0 at the 0.05 level of significance? A) fail to reject H 0 B) not sufficient information to decide C) reject H 0 49358) A bottling company needs to produce bottles that will hold 8 ounces of liquid for a local brewery. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 64 bottles and finds the average amount of liquid held by the 64 bottles is 7.9145 ounces with a standard deviation of 0.40 ounce. Suppose the p-value of this test turned out to be 0.0436. State the proper conclusion. A) At ? = 0.05, reject the null hypothesis. B) At ? = 0.035, accept the null hypothesis. C) At ? = 0.025, reject the null hypothesis. D) At ? = 0.085, fail to reject the null hypothesis. 359) A test of hypothesis was performed to determine if the true proportion of college students who preferred a particular soda is less than .50. The ASP printout is supplied below. Note: All data refer to the proportion of students who preferred the soda. HYPOTHESIS: PROPORTION X = x X = drink_(soda=1) SAMPLE PROPORTION OF X= 0.407186 SAMPLE SIZE OF X= 167 HYPOTHESIZED VALUE (x)= 0.5 SAMPLE PROPORTION X - x = 0.092814 Z = -2.39884 P-VALUE= 0.0164 P-VALUE/2 = 0.0082 SD. ERROR= 0.0386912 Identify the observed significance level for the desired test. A) 0.0386912 B)-2.39884 C) 0.0164 D) 0.0082 360) Consider the following printout. HYPOTHESIS: MEAN X = x X = gpa SAMPLE MEAN OF X = 2.9528 SAMPLE VARIANCE OF X = 0.226933 SAMPLE SIZE OF X = 167 HYPOTHESIZED VALUE (x) = 3 MEAN X - x = -0.0472 z = -1.2804 Suppose a two-tailed test is desired. Find the p-value for the test. A) p = 0.1003 B) p = 0.8997 C) p = 0.2006 D) p = 0.7994 50361) A national organization has been working with utilities throughout the nation to find sites for large wind machines for generating electric power. Wind speeds must average more than 14 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted tests at a particular site under construction for a wind machine. To determine whether the site meets the organization's requirements, consider the test, H 0 : µ = 14 vs. H a : µ > 14, where µ is the true mean wind speed at the site and ? = .05. Suppose the observed significance level (p-value) of the test is calculated to be p = 0.2739. Interpret this result based on the p-value of 0.2739. A) Since the p-value greatly exceeds ? = .05, there is strong evidence to reject the null hypothesis. B) We are 72.61% confident that µ = 14. C) The probability of rejecting the null hypothesis is 0.2739. D) Since the p-value exceeds ? = .05, there is insufficient evidence to reject the null hypothesis. 362) If a hypothesis test were conducted using ? = 0.10, for which of the following p-values would the null hypothesis be rejected. A) 0.090 B) 0.105 C) 0.110 D) 0.150 363) An analyst tested the null hypothesis µ = 20 against the alternative hypothesis µ < 20. The analyst reported a p-value of .07. What is the smallest value of ? for which the null hypothesis would be rejected? A) .08 B) .06 C) .09 D) .07 364) A journal article reported that for the 1998-1999 academic year, four-year private colleges charged students an average of $8446 for tuition and fees. Suppose that for 1999-2000 a random sample of 30 private colleges yielded the following data on tuition and fees: x = $9392 and s = $1643. Assume that $8446 is the population mean for 1998-1999. Suppose it is desired to determine if the average for tuition and fees exceeds the reported $8446. The p-value for the test was reported to be p = .0008. State the proper conclusion using an ? = .01. 365) Which part of the test of hypothesis procedure determines the value of the p-value? A) The test statistic. B) The sampling distribution of the test statistic. C) The alternative hypothesis. D) All of the above. Answer the question True or False. 366) The smaller the p-value in a test of hypothesis, the more significant the results are. 51Solve the problem. 367) A consumer product magazine recently ran a story concerning the increasing price of VCR's. The story stated that VCR prices dipped in the early 1990's but now are beginning to skyrocket in price. According to the story, the average price of a VCR in 1992 was$202. Use the STATISTIX printout shown below to answer the following question regarding this story. ONE-SAMPLE T TEST FOR VCR_PRICE NULL HYPOTHESIS: MU = 202 ALTERNATIVE HYP: MU > 202 MEAN 234.57 STD ERROR 16.932 MEAN - Ho 32.57 T 1.924 DF 24 P .0331 CASES INCLUDED 25 Is the sample size of n = 25 large enough to utilize the Central Limit Theorem in this inferential procedure? A) No, since n < 30. B) Yes, since the Central Limit theorem works whenever means are used. C) No, since the interval p + 3 pq/n does include the value 0 or 1. D) Yes, since the interval p + 3 pq/n does not include the value 0 or 1. 368) A consumer product magazine recently ran a story concerning the increasing price of VCR's. The story stated that VCR prices dipped in the early 1990's but now are beginning to skyrocket in price. According to the story, the average price of a VCR in 1992 was$215. Use the STATISTIX printout shown below to answer the following question regarding this story. ONE-SAMPLE T TEST FOR VCR_PRICE NULL HYPOTHESIS: MU = 215 ALTERNATIVE HYP: MU > 215 MEAN 245.23 STD ERROR 15.62 MEAN - Ho 30.23 T 1.935 DF 19 P .0340 CASES INCLUDED 20 Is the sample size of n = 20 large enough to utilize the Central Limit Theorem in this inferential procedure? A) Yes, since the Central Limit theorem works whenever means are used. B) No, since the interval p + 3 pq/n does include the value 0 or 1. C) No, since n < 30. D) Yes, since the interval p + 3 pq/n does not include the value 0 or 1. 52369) A consumer product magazine recently ran a story concerning the increasing price of VCR's. The story stated that VCR prices dipped in the early 1990's but now are beginning to skyrocket in price. According to the story, the average price of a VCR in 1992 was $226. Use the STATISTIX printout shown below to answer the following question regarding this story. ONE-SAMPLE T TEST FOR VCR_PRICE NULL HYPOTHESIS: MU = 226 ALTERNATIVE HYP: MU > 226 MEAN 256.23 STD ERROR 15.62 MEAN - Ho 30.23 T 1.935 DF 19 P .0340 CASES INCLUDED 20 What assumption must be satisfied in order for these results to be valid? A) The population of all VCR prices must posses an approximately normal distribution. B) The population of all VCR prices must posses an approximate t distribution with 19 degrees of freedom. C) The sample of 20 VCR prices must posses an approximate t distribution with 19 degrees of freedom. D) The sampling distribution of the sample mean must posses an approximately normal distribution. 370) A consumer product magazine recently ran a story concerning the increasing price of VCR's. The story stated that VCR prices dipped in the early 1990's but now are beginning to skyrocket in price. According to the story, the average price of a VCR in 1992 was $201. Use the STATISTIX printout shown below to answer the following question regarding this story. ONE-SAMPLE T TEST FOR VCR_PRICE NULL HYPOTHESIS: MU = 201 ALTERNATIVE HYP: MU > 201 MEAN 231.23 STD ERROR 15.62 MEAN - Ho 30.23 T 1.935 DF 19 P .0340 CASES INCLUDED 20 Find the rejection region appropriate for this test if we are using ? = .05. A) Reject H 0 if t > 1.725 B) Reject H 0 if t > 2.086 or t < -2.086 C) Reject H 0 if t > 1.729 D) Reject H 0 if t > 2.093 or t < -2.093 53371) A consumer product magazine recently ran a story concerning the increasing price of VCR's. The story stated that VCR prices dipped in the early 1990's but now are beginning to skyrocket in price. According to the story, the average price of a VCR in 1992 was $214. Use the STATISTIX printout shown below to answer the following question regarding this story. ONE-SAMPLE T TEST FOR VCR_PRICE NULL HYPOTHESIS: MU = 214 ALTERNATIVE HYP: MU > 214 MEAN 244.23 STD ERROR 15.62 MEAN - Ho 30.23 T 1.935 DF 19 P .0340 CASES INCLUDED 20 Use the p-value given above to determine the correct conclusion. A) At ? = .05, there is sufficient evidence to indicate that the mean price of VCR's exceeds $214. B) At ? = .01, there is sufficient evidence to indicate that the mean price of VCR's exceeds $214. C) At ? = .10, there is insufficient evidence to indicate that the mean price of VCR's exceeds $214. D) At ? = .05, there is insufficient evidence to indicate that the mean price of VCR's exceeds $214. 372) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 37 minutes. The owner has randomly selected 19 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 37 minutes. What assumption is necessary for this test to be valid? A) The population of delivery times must have a normal distribution. B) The sample mean delivery time must equal the population mean delivery time. C) The population variance must equal the population mean. D) None. The Central Limit Theorem makes any assumptions unnecessary. 373) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 36 minutes. The owner has randomly selected 15 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 36 minutes. Suppose the p-value for the test was found to be .0272. State the correct conclusion. A) At ? = .025, we fail to reject H 0 . B) At ? = .02, we reject H 0 . C) At ? = .05, we fail to reject H 0 . D) At ? = .03, we fail to reject H 0 . 54374) Data were collected from the sale of 25 properties by a local real estate agent. The following printout concentrated on the land value variable from the sampled properties. HYPOTHESIS: MEAN X = x X = land_value SAMPLE MEAN OF X = 46,357 SAMPLE VARIANCE OF X = 273,643,254 SAMPLE SIZE OF X = 25 x = 41,914 MEAN X - x = 4443 t = 1.34293 D.F. = 24 P-VALUE = 0.1918585 P-VALUE/2 = 0.0959288 SD. ERROR = 3308.43 Suppose we are interested in testing whether the mean land value from this neighborhood differs from 41,914. Which hypotheses would you test? A) H 0 : µ = 41,914 vs. H a : µ ? 41,914 B) H 0 : µ = 41,914 vs. H a : µ > 41,914 C) H 0 : µ ? 41,914 vs. H a : µ = 41,914 D) H 0 : µ = 41,914 vs. H a : µ < 41,914 375) Data were collected from the sale of 25 properties by a local real estate agent. The following printout concentrated on the land value variable from the sampled properties. HYPOTHESIS: MEAN X = x X = land_value SAMPLE MEAN OF X = 53,746 SAMPLE VARIANCE OF X = 273,643,254 SAMPLE SIZE OF X = 25 x = 49,303 MEAN X - x = 4443 t = 1.34293 D.F. = 24 P-VALUE = 0.1918585 P-VALUE/2 = 0.0959288 SD. ERROR = 3308.43 Find the p-value for testing whether the mean land value differs from $49,303. A) p = 0.308142 B) p = 0.808142 C) p = 0.0959288 D) p = 0.1918585 55376) Data were collected from the sale of 25 properties by a local real estate agent. The following printout concentrated on the land value variable from the sampled properties. HYPOTHESIS: MEAN X = x X = land_value SAMPLE MEAN OF X = 47,216 SAMPLE VARIANCE OF X = 273,643,254 SAMPLE SIZE OF X = 25 x = 42,773 MEAN X - x = 4443 t = 1.34293 D.F. = 24 P-VALUE = 0.1918585 P-VALUE/2 = 0.0959288 SD. ERROR = 3308.43 What is the correct conclusion when testing a greater-than alternative hypothesis at ? = .01? A) Fail to reject H 0 . B) Accept H 0 . C) Fail to reject H a . D) Reject H 0 . 377) Data were collected from the sale of 25 properties by a local real estate agent. The following printout concentrated on the land value variable from the sampled properties. HYPOTHESIS: MEAN X = x X = land_value SAMPLE MEAN OF X = 53,180 SAMPLE VARIANCE OF X = 273,643,254 SAMPLE SIZE OF X = 25 x = 48,737 MEAN X - x = 4443 t = 1.34293 D.F. = 24 P-VALUE = 0.1918585 P-VALUE/2 = 0.0959288 SD. ERROR = 3308.43 What assumptions are necessary for any inferences derived from this printout to be valid? A) The sample was selected from an approximately normal population. B) The sampled data are approximately normal. C) None. The Central Limit Theorem makes any assumptions unnecessary. D) The sampling distribution of the sample mean is approximately normal. 56378) A local tennis pro-shop strings tennis rackets at the tension (pounds per square inch) requested by the customer. Recently a customer made a claim that the pro-shop consistently strings rackets at lower tensions, on average, than requested. To support this claim, the customer asked the pro shop to string 10 new rackets at 46 psi. Suppose the two-tailed p-value for the test described above (obtained from a computer printout) is p = .09. Give the proper conclusion for the test. Use ? = .05. A) Reject H 0 and conclude that µ, the true mean tension of the rackets, equals 46 psi. B) There is sufficient evidence to conclude that µ, the true mean tension of the rackets, is less than 46 psi. C) Accept H 0 and conclude that µ, the true mean tension of the rackets, equals 46 psi. D) There is insufficient evidence to conclude that µ, the true mean tension of the rackets, is less than 46 psi. 379) A local tennis pro-shop strings tennis rackets at the tension (pounds per square inch) requested by the customer. Recently a customer made a claim that the pro-shop consistently strings rackets at lower tensions, on average, than requested. To support this claim, the customer asked the pro shop to string 7 new rackets at 42 psi. Upon receiving the rackets, the customer measured the tension of each and calculated the following summary statistics: x = 41 psi, s = 3.4 psi. What assumptions about the distribution of racket tensions are necessary for the inferences derived from this test to be valid? A) The sampling distribution of mean racket tensions is approximately normally distributed. B) None. The Central Limit Theorem guarantees that the sampling distribution of x will be normal. C) The population of racket tensions is approximately normally distributed. D) The sample variance must equal the population variance. 380) An industrial supplier has shipped a truckload of teflon lubricant cartridges to an aerospace customer. The customer has been assured that the mean weight of these cartridges is in excess of the 13 ounces printed on each cartridge. To check this claim, a sample of n = 25 cartridges are randomly selected from the shipment and carefully weighed. Summary statistics for the sample are: x = 13.16 ounces, s = .25 ounce. To determine whether the supplier's claim is true, consider the test, H 0 : µ = 13 vs. H a : µ > 13, where µ is the true mean weight of the cartridges. Calculate the value of the test statistic. A) 16.000 B) 1.600 C) 0.640 D) 3.200 381) An industrial supplier has shipped a truckload of teflon lubricant cartridges to an aerospace customer. The customer has been assured that the mean weight of these cartridges is in excess of the 10 ounces printed on each cartridge. To check this claim, a sample of n = 10 cartridges are randomly selected from the shipment and carefully weighed. Summary statistics for the sample are: x = 10.11 ounces, s = .30 ounce. To determine whether the supplier's claim is true, consider the test, H 0 : µ = 10 vs. H a : µ > 10, where µ is the true mean weight of the cartridges. Find the rejection region for the test using ? = .01. A) | z | > 2.58 B) t > 3.25, where t depends on 9 df C) z > 2.33 D) t > 2.821, where t depends on 9 df 382) A bottling company needs to produce bottles that will hold 10 ounces of liquid for a local brewery. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 17 bottles and finds the average amount of liquid held by the 17 bottles is 9.8 ounces with a standard deviation of .4 ounce. Which of the following is the set of hypotheses the company wishes to test? A) H 0 : µ = 10 vs. H a : µ < 10 B) H 0 : µ = 10 vs. H a : µ ? 10 C) H 0 : µ = 10 vs. H a : µ > 10 D) H 0 : µ < 10 vs. H a : µ = 10 57383) A bottling company needs to produce bottles that will hold 10 ounces of liquid for a local brewery. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 25 bottles and finds the average amount of liquid held by the 25 bottles is 9.6 ounces with a standard deviation of .2 ounce. Calculate the appropriate test statistic. A) t = -4.472 B) t = -10.000 C) t = -50.000 D) t = -9.798 384) A consumer product magazine recently ran a story concerning the increasing price of VCR's. The story stated that VCR prices dipped in the early 1990's but now are beginning to skyrocket in price. According to the story, the average price of a VCR in 1992 was $209. A sample of 16 VCR's in 1998 yielded an average price of $279 and a standard deviation of $70. Test to determine if the average price of VCR's in 1998 exceeds the average price in 1992. Use ? = .05. 385) According to advertisements, a strain of soybeans planted on soil prepared with a specified fertilizer treatment has a mean yield of 99 bushels per acre. Twenty-five farmers who belong to a cooperative plant the soybeans. Each uses a 40-acre plot and records the mean yield per acre. The mean and variance for the sample of the 25 farms are x = 84 and s 2 = 28,125. Find the rejection region used for determining if the mean yield for the soybeans is equal to 99 bushels per acre. Use ? = .05. 386) A test of hypothesis was performed to determine if the true proportion of college students who preferred a particular brand of soda differs from .50. The ASP printout is supplied below. Note: All data refer to the proportion of students who preferred the brand of soda. HYPOTHESIS: PROPORTION X = x X = drink_(soda=1) SAMPLE PROPORTION OF X = .419162 SAMPLE SIZE OF X = 167 HYPOTHESIZED VALUE (x) = .5 SAMPLE PROPORTION X - x = -.080838 Z = -2.08932 P-VALUE = .0366 P-VALUE/2 = .0183 SD. ERROR = .0386912 Based on the interval above, where would the 99% confidence interval for the true proportion be located? A) completely above .5 B) completely below .5 C) with .5 contained in the interval D) cannot tell from this test of hypothesis printout 387) The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion exceeds 30%, then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business students were randomly sampled and 75 have PC's at home. Find the rejection region for this test using ? = .05. A) Reject H 0 if z = 1.645. B) Reject H 0 if z > 1.645. C) Reject H 0 if z > 1.96 or z < -1.96. D) Reject H 0 if z < -1.645. 58388) The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion differs from 35%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is 2.6. Find the p-value for a two-tailed test of hypothesis. A) .4953 B) .4906 C) .0094 D) .0047 389) The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion exceeds 25%, then the lab will scale back a proposed enlargement of its facilities. Suppose 200 business students were randomly sampled and 65 have PC's at home. What assumptions are necessary for this test to be satisfied? A) The population has an approximately normal distribution. B) The sample mean equals the population mean. C) The sample variance equals the population variance. D) None of the above are necessary. 390) A survey claims that 9 out of 10 doctors (i.e., 90%) recommend brand Z for their patients who have children. To test this claim against the alternative that the actual proportion of doctors who recommend brand Z is less than 90%, a random sample of 100 doctors results in 87 who indicate that they recommend brand Z. The test statistic in this problem is approximately: A) 1.00 B)-0.66 C)-0.50 D)-1.00 391) A survey claims that 9 out of 10 doctors (i.e., 90%) recommend brand Z for their patients who have children. To test this claim against the alternative that the actual proportion of doctors who recommend brand Z is less than 90%, a random sample of doctors was taken. Suppose the test statistic is z = -1.95. Can we conclude that H 0 should be rejected at the a) ? = .10, b) ? = .05, and c) ? = .01 level? A) a) yes; b) yes; c) no B) a) no; b) no; c) no C) a) no; b) no; c) yes D) a) yes; b) yes; c) yes 59392) A test of hypothesis was performed to determine if the true proportion of college students who preferred a particular brand of soda differs from .50. The ASP printout is supplied below. Note: All data refer to the proportion of students who preferred the brand of soda. HYPOTHESIS: PROPORTION X = x X = drink_(soda=1) SAMPLE PROPORTION OF X = .431138 SAMPLE SIZE OF X = 167 HYPOTHESIZED VALUE (x) = .5 SAMPLE PROPORTION X - x = -.068862 Z = -1.77979 P-VALUE = .0750 P-VALUE/2 = .0375 SD. ERROR = .0386912 State the proper conclusion if the test was conducted at ? = .01. A) There is sufficient evidence to indicate the true proportion of college students who prefer the brand of soda is equal to .50. B) There is sufficient evidence to indicate the true proportion of college students who prefer the brand of soda is less than .50. C) There is insufficient evidence to indicate the true proportion of college students who prefer the brand of soda is less than .50. D) There is sufficient evidence to indicate the true proportion of college students who prefer the brand of soda differs from .50. 393) A test of hypothesis was performed to determine if the true proportion of college students who preferred a particular brand of soda differs from .50. The ASP printout is supplied below. Note: All data refer to the proportion of students who preferred the brand of soda. HYPOTHESIS: PROPORTION X = x X = drink_(soda=1) SAMPLE PROPORTION OF X = .407186 SAMPLE SIZE OF X = 167 HYPOTHESIZED VALUE (x) = .5 SAMPLE PROPORTION X - x = -.092814 Z = -2.39884 P-VALUE = .0164 P-VALUE/2 = .0082 SD. ERROR = .0386912 Based on the interval above, where would the 99% confidence interval for the true proportion be located? A) completely below .5 B) cannot tell from this test of hypothesis printout C) with .5 contained in the interval D) completely above .5 60394) A test of hypothesis was performed to determine if the true proportion of college students who preferred a particular brand of soda differs from .50. The ASP printout is supplied below. Note: All data refer to the proportion of students who preferred the brand of soda. HYPOTHESIS: PROPORTION X = x X = drink_(soda=1) SAMPLE PROPORTION OF X = .419162 SAMPLE SIZE OF X = 167 HYPOTHESIZED VALUE (x) = .5 SAMPLE PROPORTION X - x = -.080838 Z = -2.08932 P-VALUE = .0366 P-VALUE/2 = .0183 SD. ERROR = .0386912 What assumptions are necessary for any inferences derived from this printout to be valid? A) The sample proportion equals the population proportion. B) The population proportion has an approximate normal distribution. C) The sample was randomly selected from an approximately normal population. D) None of these assumptions are necessary. 395) It is desired to estimate the proportion of college students who prefer brand A over brand B. A random sample of 75 students was collected. ASP was used to test whether the proportion of all college students who preferred brand B is smaller than 40%. HYPOTHESIS: PROPORTION X = x X = brand A-0_or_brand B-1 SAMPLE PROPORTION OF X = .386667 SAMPLE SIZE OF X = 75 x = .4 SAMPLE PROPORTION X - x = -.013333 Z = .23570 P-VALUE = ..8886 P-VALUE/2 = .4052 SD. ERROR = .0566 Is the sample size large enough to use the Central Limit Theorem? A) Yes, since the interval p 0 ± 3 p 0 (1 - p 0 )/n does not contain 0 or 1. B) Yes, since n > 30. C) No, since the Central Limit Theorem is not used with proportions. D) No, since the population is not approximately normal. 61396) It is desired to estimate the proportion of college students who prefer brand A over brand B. A random sample of 71 students was collected. ASP was used to test whether the proportion of all college students who preferred brand B is smaller than 40%. HYPOTHESIS: PROPORTION X = x X = brand A-0_or_brand B-1 SAMPLE PROPORTION OF X = .366197 SAMPLE SIZE OF X = 71 x = .4 SAMPLE PROPORTION X - x = -.033803 Z = .58140 P-VALUE = ..5620 P-VALUE/2 = .2810 SD. ERROR = .0581 Interpret the p-value for the test that is desired. A) At ? = .10, there is insufficient evidence to indicate that the proportion of college students who prefer brand B is smaller than 40%. B) At ? = .10, there is sufficient evidence to indicate that the proportion of college students who prefer brand B is smaller than to 40%. C) At ? = .10, there is insufficient evidence to indicate that the proportion of college students who prefer brand B is equal to 36.6197%. D) At ? = .10, there is sufficient evidence to indicate that the proportion of college students who prefer brand B is equal to 36.6197%. 397) It is desired to estimate the proportion of college students who prefer brand A over brand B. A random sample of 71 students was collected. ASP was used to test whether the proportion of all college students who preferred brand B is smaller than 40%. HYPOTHESIS: PROPORTION X = x X = brand A-0_or_brand B-1 SAMPLE PROPORTION OF X = .366197 SAMPLE SIZE OF X = 71 x = .4 SAMPLE PROPORTION X - x = -.033803 Z = .58140 P-VALUE = .5620 P-VALUE/2 = .2810 SD. ERROR = .0581 When estimating the true standard error for the test statistic, what value will be used to estimate the unknown population proportion? A) .40 B) .50 C) .24 D) .366197 62398) A nationwide survey claimed that at least 65% of parents with young children condone spanking their child as a regular form of punishment. In a random sample of 100 parents with young children, how many would need to say that they condone spanking as a form of punishment in order to refute the claim at ? = 0.5? A) You would need 58 or less parents to support spanking to refute the claim. B) You would need 57 or less parents to support spanking to refute the claim. C) You would need more than 57 parents to support spanking to refute the claim. D) You would need exactly 57 parents to support spanking to refute the claim. 399) A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 15% of the women who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 60 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in 7. Calculate the test statistic used by the researchers for this test of hypothesis. 400) A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 20% of the women who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 80 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in 9. Is the sample size sufficiently large in order to conduct this test of hypothesis? Explain. 401) Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that more than 85% of firms in the manufacturing sector still do not offer any child-care benefits to their workers. A random sample of 300 manufacturing firms is selected, and only 32 of them offer child-care benefits. Specify the rejection region that the union will use when testing at ? = .10. 402) Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that more than 80% of firms in the manufacturing sector still do not offer any child-care benefits to their workers. A random sample of 350 manufacturing firms is selected and asked if they offer child-care benefits. Suppose the p-value for this test was reported to be p = .1130. State the conclusion of interest to the union. Use ? = .05. 403) I want to test H 0 : p = .7 vs. H a : p ? .7 using a test of hypothesis. This test would be called a(n) ____________ test. A) two-tailed B) lower-tailed C) one-tailed D) upper-tailed 404) It has been estimated that the 2000 G-car obtains a mean of 30 miles per gallon on the highway, and the company that manufactures the car claims that it exceeds this estimate in highway driving. To support its assertion, the company randomly selects 49, 2000 G-cars and records the mileage obtained for each car over a driving course similar to that used to obtain the estimate. The following data resulted: x = 31.5 miles per gallon, s = 7 miles per gallon. Calculate the power of the test if the true value of the mean is really 31 miles per gallon. Use a value of ? = .025. 405) It is desired to test H 0 : µ = 45 against H a : µ < 45 using ? = 0.10. The population in question is uniformly distributed with a standard deviation of 15. A random sample of 49 will be drawn from this population. If µ is really equal to 40, what is the probability that the hypothesis test would lead the investigator to commit a Type II error? A) .8531 B) .1469 C) .3531 D) .2938 63406) It is desired to test H 0 : µ = 55 against H a : µ < 55 using ? = 0.10. The population in question is uniformly distributed with a standard deviation of 20. A random sample of 64 will be drawn from this population. What is the power of this test? A) .5284 B) .2358 C) .7642 D) .2642 407) It is desired to test H 0 : µ = 12 against H a : µ ? 12 using ? = 0.05. The population in question is uniformly distributed with a standard deviation of 2.0. A random sample of 100 will be drawn from this population. If µ is really equal to 11.9, what is the value of ß associated with this test? A) .0395 B) .9210 C) .0790 D) .4210 408) It has been estimated that the 2000 G-car obtains a mean of 30 miles per gallon on the highway, and the company that manufactures the car claims that it exceeds this estimate in highway driving. To support its assertion, the company randomly selects 49, 2000 G-cars and records the mileage obtained for each car over a driving course similar to that used to obtain the estimate. The following data resulted: x = 31.8 miles per gallon, s = 7 miles per gallon. Calculate the power of the test if the true value of the mean is really 31 miles per gallon. Use a value of ? = .025. 409) It has been estimated that the 1991 G-car obtains a mean of 30 miles per gallon on the highway, and the company that manufactures the car claims that it exceeds this estimate in highway driving. To support its assertion, the company randomly selects 49 1991 G-cars and records the mileage obtained for each car over a driving course similar to that used to obtain the estimate. The following data resulted: x = 31.2 miles per gallon, s = 7 miles per gallon. Calculate the value of ß if the true value of the mean is really 32 miles per gallon. Use ? = .025. 410) A new apparatus has been devised to replace the needle in administering vaccines. The apparatus, which is connected to a large supply of vaccine, can be set to inject different amounts of the serum, but the variance in the amount of serum injected to a given person must not be greater than .0 7 to ensure proper inoculation. A random sample of 36 injections resulted in a variance of .103. Calculate the test statistic for the test of interest. 411) Let ? 2 0 be a particular value of ? 2 . Find the value of ? 2 0 such that P( ? 2 > ? 2 0 ) = 0.10 for n = 10. A) 14.6837 B) 16.919 C) 15.9871 D) 4.16816 412) An educational testing service designed an achievement test so that the range in student scores would be at least 420 points. To determine whether the objective was achieved, the testing service gave the test to a random sample of 47 students and found that the sample mean and variance were 673 and 2350, respectively. Specify the null and alternative hypotheses for determining whether the test achieved the desired dispersion in scores. Assume that range = 6?. 413) An educational testing service designed an achievement test so that the range in student scores would be at least 420 points. To determine whether the objective was achieved, the testing service gave the test to a random sample of 30 students and found that the sample mean and variance were 759 and 1943, respectively. Conduct the test for H 0 : ? 2 = 4900 vs. H a : ? 2 > 4900 using ? = .025. Assume the range is 6?. 414) A new apparatus has been devised to replace the needle in administering vaccines. The apparatus, which is connected to a large supply of vaccine, can be set to inject different amounts of the serum, but the variance in the amount of serum injected to a given person must not be greater than .0 5 to ensure proper inoculation. A random sample of 25 injections resulted in a variance of .118. Calculate the test statistic for the test of interest. 64415) A new apparatus has been devised to replace the needle in administering vaccines. The apparatus, which is connected to a large supply of vaccine, can be set to inject different amounts of the serum, but the variance in the amount of serum injected to a given person must not be greater than .0 6 to ensure proper inoculation. A random sample of 41 injections resulted in a variance of .103. Specify the rejection region for the test. Use ? = .10. 416) A new apparatus has been devised to replace the needle in administering vaccines. The apparatus, which is connected to a large supply of vaccine, can be set to inject different amounts of the serum, but the variance in the amount of serum injected to a given person must not be greater than .0 6 to ensure proper inoculation. A random sample of 49 injections was measured. Suppose the p-value for the test is p = .0031. State the proper conclusion using ? = .01. 417) A random sample of n observations, selected from a normal population, is used to test the null hypothesis H 0 : ? 2 = 155. Specify the appropriate rejection region. H a : ? 2 < 155, n = 14, ? = .01 A) x 2 < 4.10691 B) x 2 < 4.66043 C) x 2 < 29.1413 D) x 2 < 27.6883 418) A random sample of n observations, selected from a normal population, is used to test the null hypothesis H 0 : ? 2 = 155. Specify the appropriate rejection region. H a : ? 2 ? 155, n = 10, ? = .05 A) x 2 < 2.70039 or x 2 > 19.0228 B) x 2 < 3.32511 or x 2 > 16.9190 C) 2.70039 < x 2 < 19.0228 D) x 2 < 3.24697 or x 2 > 20.4831 419) A random sample of n observations, selected from a normal population, is used to test the null hypothesis H 0 : ? 2 = 155. Specify the appropriate rejection region. H a : ? 2 > 155, n = 25, ? = .10 A) x 2 > 33.1963 B) x 2 > 15.6587 C) x 2 > 36.4151 D) x 2 > 34.3816 420) During the last 10 years marketing executives believed that the same proportion of adult men and adult women watched TV news programs. Current information indicates there has been an increase in the percentage of women watching TV news programs. The marketing executives would like to perform a statistical test to assure themselves that a greater proportion of women now watch TV news programs than men. What should be used for the Null and Alternative hypotheses to perform this test? A) H 0 : P W - P M = 0 vs. H a : P W - P M ? 0 B) H 0 : P W - P M = 0 vs. H a : P W - P M > 0 C) H 0 : P µ - P µ = 0 vs. H a : P µ - P µ > 0 D) H 0 : P = .5 vs. H a : P ? .5 E) H 0 : P W - P M < 0 vs. H a : P W - P M = 0 65421) All convenience stores in the Tampa area are allowed to set their own price for six packs of cola. We are interested in comparing the prices of two leading colas in the Tampa area. Our sample was taken by randomly going to each of 8 convenience stores and recording the price of a six-pack of cola of each brand. The data is shown in the following table. What type of analysis should be used to allow us to determine if there is a difference in the average price between the two brands of cola. Supermarket Price Brand 1 Brand 2 1 $3.25 $3.30 2 3.47 3.45 3 2.50 2.99 4 3.27 2.89 5 2.55 2.95 6 3.25 3.25 7 3.30 3.42 8 3.39 2.50 x = 3.1225 x = 3.09375 A) A test comparing two population means with paired difference or matched pairs. B) A test of two population proportions with independent sampling. C) An independent sample of a single population mean. D) A test comparing two experiments with correlated but independent factors. E) A test comparing two population means with independent samples. 422) A shoe manufacturer has developed a new technology that will make tennis shoes last much longer than the current technology enables. The technology involves a thin layer of a new chemical that is applied to the sole of the shoe after the production process is complete. To test this new technology, 55 tennis players were randomly selected. Each tennis player is given a new set of tennis shoes, only one of which is treated with the new chemical. Each tennis player is then asked to record the number of hours of wear before each shoe wears out. For each tennis player, both a treated and untreated hours of wear measurement is recorded. The results were then compared across all tennis players. Some of the data appear below: Tennis Player Treated Shoe Untreated Shoe 1 213 185 2 305 265 · · · · · · What type of analysis will best allow the shoe manufacturer to determine if the new technology is effective? A) A paired difference comparison of population means. B) A test of a single population proportion. C) An independent samples comparison of population means. D) An independent samples comparison of population proportions. 66423) A shoe manufacturer has developed a new technology that will make tennis shoes last much longer than the current technology enables. The technology involves a thin layer of a new chemical that is applied to the sole of the shoe after the production process is complete. To test this new technology, 55 tennis players were randomly selected. Each tennis player is given a new set of tennis shoes, only one of which is treated with the new chemical. Each tennis player is then asked to record the number of hours of wear before each shoe wears out. For each tennis player, both a treated and untreated hours of wear measurement is recorded. The results were then compared across all tennis players. Some of the data appear below: Tennis Player Treated Shoe Untreated Shoe 1 213 185 2 305 265 · · · · · · Which of the following confidence intervals would indicate that the new technology is effective in increasing the mean wear of the tennis shoes? Assume we are comparing in the order (Treated - Untreated). A) (-3.5, 85.6) B) (-25.6, -2.6) C) (45.3, 55.6) D) (-10.5, 36.5) 424) A shoe manufacturer has developed a new technology that will make tennis shoes last much longer than the current technology enables. The technology involves a thin layer of a new chemical that is applied to the sole of the shoe after the production process is complete. To test this new technology, 55 tennis players were randomly selected. Each tennis player is given a new set of tennis shoes, only one of which is treated with the new chemical. Each tennis player is then asked to record the number of hours of wear before each shoe wears out. For each tennis player, both a treated and untreated hours of wear measurement is recorded. The results were then compared across all tennis players. Some of the data appear below: Tennis Player Treated Shoe Untreated Shoe 1 213 185 2 305 265 · · · · · · What assumptions are necessary for the above test to be valid? A) Both populations must be approximately normally distributed. B) None of these listed, since the Central Limit Theorem can be applied. C) The population variances must be approximately normally distributed. D) The population of paired differences must be approximately normally distributed. 67425) We are interested in comparing the average supermarket prices of two leading colas in the Tampa area. Our sample was taken by randomly going to each of eight supermarkets and recording the price of a six-pack of cola of each brand. The data are shown in the following table: Price Supermarket Brand 1 Brand 2 Difference 1 $2.25 $2.30 $-0.05 2 2.47 2.45 0.02 3 2.38 2.44 -0.06 4 2.27 2.29 -0.02 5 2.15 2.25 -0.10 6 2.25 2.25 0.00 7 2.36 2.42 -0.06 8 2.37 2.40 -0.03 x 1 = 2.3125 s 1 = 0.1007 x 2 = 2.3500 s 2 = 0.0859 d = -0.0375 s d = 0.0381 Find a 98% confidence interval for the difference in mean price of brand 1 and brand 2. A) 0.0375 ± 0.0347 B) 0.0375 ± 0.1393 C) 0.0375 ± 0.0471 D) 0.0375 ± 0.0404 426) We are interested in comparing the average supermarket prices of two leading colas in the Tampa area. Our sample was taken by randomly going to each of eight supermarkets and recording the price of a six-pack of cola of each brand. The data are shown in the following table: Price Supermarket Brand 1 Brand 2 Difference 1 $2.25 $2.30 $-0.05 2 2.47 2.45 0.02 3 2.38 2.44 -0.06 4 2.27 2.29 -0.02 5 2.15 2.25 -0.10 6 2.25 2.25 0.00 7 2.36 2.42 -0.06 8 2.37 2.40 -0.03 x 1 = 2.3125 s 1 = 0.1007 x 2 = 2.3500 s 2 = 0.0859 d = -0.0375 s d = 0.0381 Suppose the interval above turned out to be (0.04, 0.07) (not the correct answer). Which of the following would be a correct interpretation of this interval? A) We are 99% confident that the brands' average cost is equal. B) We are 99% confident that brand 1 is more expensive than brand 2. C) We are 99% confident that brand 2 is more expensive than brand 1. 68427) We are interested in comparing the average supermarket prices of two leading colas in the Tampa area. Our sample was taken by randomly going to each of eight supermarkets and recording the price of a six-pack of cola of each brand. The data are shown in the following table: Price Supermarket Brand 1 Brand 2 Difference 1 $2.25 $2.30 $-0.05 2 2.47 2.45 0.02 3 2.38 2.44 -0.06 4 2.27 2.29 -0.02 5 2.15 2.25 -0.10 6 2.25 2.25 0.00 7 2.36 2.42 -0.06 8 2.37 2.40 -0.03 x 1 = 2.3125 s 1 = 0.1007 x 2 = 2.3500 s 2 = 0.0859 d = -0.0375 s d = 0.0381 If the problem above represented a matched pairs experiment (which may or may not be true), what assumptions are needed for the confidence interval above to be valid? A) The population of paired differences has an approximate normal distribution. B) The population variances are equal. C) The samples were independently selected from one another. D) All of the above are needed. 428) Which supermarket has the lowest prices in town? All claim to be cheaper, but an independent agency was asked to investigate this question. The agency randomly selected 100 items common to each of two supermarkets (labelled A and B for confidentiality) and recorded the prices charged by each supermarket. The summary results are provided below: xA = 2.09 xB = 1.99 d = .10 s A = 0.22 s B = 0.19 s d = .03 Based on the way the data is described, this experiment is a(n) _________. A) completely randomized design B) independent samples design C) matched pairs design 429) Which supermarket has the lowest prices in town? All claim to be cheaper, but an independent agency recently was asked to investigate this question. The agency randomly selected 100 items common to each of two supermarkets (labelled A and B for confidentiality) and recorded the prices charged by each supermarket. The summary results are provided below: xA = 2.09 xB = 1.99 d = .10 s A = 0.22 s B = 0.19 s d = .03 Assuming the data represent a matched pairs design, calculate the confidence interval for comparing mean prices using a 95% confidence level. A) .10 ± .004935 B) .10 ± .00588 C) .10 ± .056975 D) .10 ± .1255 69430) Which supermarket has the lowest prices in town? All claim to be cheaper, but an independent agency recently was asked to investigate this question. The agency randomly selected 100 items common to each of two supermarkets (labelled A and B for confidentiality) and recorded the prices charged by each supermarket. The summary results are provided below: xA = 2.09 xB = 1.99 d = .10 s A = 0.22 s B = 0.19 s d = .03 Suppose the true interval turned out to be (-.12, .02). Which of the following interpretations is correct? A) None of these interpretations is correct. B) We are 95% confident that µ A equals µ B . C) We are 95% confident that µ A is larger than µ B . D) We are 95% confident that µ B is larger than µ A . 431) Which supermarket has the lowest prices in town? All claim to be cheaper, but an independent agency recently was asked to investigate this question. The agency randomly selected 100 items common to each of two supermarkets (labelled A and B for confidentiality) and recorded the prices charged by each supermarket. The summary results are provided below: xA = 2.09 xB = 1.99 d = .10 s A = 0.22 s B = 0.19 s d = .03 Assuming a matched pairs design, which assumptions are necessary for this confidence interval to be valid? A) The samples are randomly and independently selected. B) The population of paired differences has an approximate normal distribution. C) The population variances must be equal. D) None of these assumptions are necessary. 432) A researcher wanted to investigate which of two newly developed automobile engine oils (A or B) is better at prolonging the life of the engine. Since there are a variety of automobile engines that are used in today's cars, 20 different engine types were randomly selected and were tested using each of the two engine oils. The number of hours of continuous use before engine breakdown was recorded for each engine oil. Based on the information provided, what type of analysis will yield the most useful information? A) Independent samples comparison of population proportions. B) Independent samples comparison of population means. C) Matched pairs comparison of population means. D) Matched pairs comparison of population proportions. 433) A researcher wanted to investigate which of two newly developed automobile engine oils (A or B) is better at prolonging the life of the engine. Since there are a variety of automobile engines that are used in today's cars, 20 different engine types were randomly selected and were tested using each of the two engine oils. The number of hours of continuous use before engine breakdown was recorded for each engine oil. Suppose the following 95% confidence interval for µ A - µ B was calculated: (100, 2500). Which of the following inferences is correct? A) We are 95% confident that no significant differences exists in the mean number of hours of continuous use before breakdown of engine oils A and B. B) We are 95% confident that engine oil B has a higher mean number of hours of continuous use before breakdown than does engine oil A. C) We are 95% confident that the mean number of hours of continuous use of engine oil A is between 100 and 2500 hours. D) We are 95% confident that engine oil A has a higher mean number of hours of continuous use before breakdown than does engine oil B. 70434) A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. A typical test performed by the FDA is the following: The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let µ 1 be the true mean weight of individuals before starting the diet and let µ 2 be the true mean weight of individuals after 3 weeks on the diet. Person Weight Before Diet Weight After Diet 1 156 149 2 201 196 3 194 191 4 203 197 5 210 206 Summary information is as follows: d = 5, s d = 1.58. Calculate a 90% confidence interval for the difference between the mean weights before and after the diet is used. 435) A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. A typical test performed by the FDA is the following: The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let µ 1 be the true mean weight of individuals before starting the diet and let µ 2 be the true mean weight of individuals after 3 weeks on the diet. Person Weight Before Diet Weight After Diet 1 148 141 2 193 188 3 186 183 4 195 189 5 202 198 Summary information is as follows: d = 5, s d = 1.58. Test to determine if the diet is effective at reducing weight. Use ? = .10. 71436) An industrial plant wants to determine which of two types of fuel (gas or electric) will produce more useful energy at a lower cost. One measure used is plant investment per delivered quad ($ invested /quadrillion BTUs). The smaller this number, the less an industrial plant pays for delivered energy. Random samples of 11 plants using electrical utilities and 16 plants using gas utilities were taken, and the plant investment/quad was calculated for each. An analysis was made of the difference of means of the two samples using a software package. Suppose we wish to determine if there was evidence to indicate a difference in the average investment/quad between plants using electrical utilities and those using gas utilities. Our null and alternative hypotheses would be: A) H 0 : (µ e - µ g ) = 0 vs. H a : (µ e - µ g ) > 0 B) H 0 : (µ e - µ g ) = 0 vs. H a : (µ e - µ g ) = 0 C) H 0 : (µ e - µ g ) = 0 vs. H a : (µ e - µ g ) < 0 D) H 0 : (µ e - µ g ) = 0 vs. H a : (µ e - µ g ) ? 0 E) None of the above. 437) An industrial plant wants to determine which of two types of fuel (gas or electric) will produce more useful energy at a lower cost. One measure used is plant investment per delivered quad ($ invested /quadrillion BTUs). The smaller this number, the less an industrial plant pays for delivered energy. Random samples of 11 plants using electrical utilities and 16 plants using gas utilities were taken, and the plant investment/quad was calculated for each. An analysis was made of the difference of means of the two samples using a software package. If we are able to Reject Ho in the test H 0 : (µ E - µ G ) = 0 vs. H a : (µ E - µ G ) > 0, our best interpretation of the result would be: A) The mean investment/quad for electric utilities is less than the mean investment/quad for gas utilities. B) The mean investment/quad for electric utilities is different from the mean investment/quad for gas utilities. C) The mean investment/quad for electric utilities is not different from the mean investment/quad for gas utilities. D) The mean investment/quad for electric utilities is greater than the mean investment/quad for gas utilities. 72438) When blood levels are low at an area hospital, a call goes out to local residents to give blood. The blood center is interested in determining which sex, males or females, is more likely to respond. Random independent samples of 60 females and 100 males produce the following results. A success is defined as a person who responds to the call and donates blood. The computer printout for this analysis appears below: TWO-SAMPLE PROPORTION TEST SAMPLE 1 SAMPLE 2 SAMPLE SIZE 60 100 SUCCESSES 45 60 PROPORTION 0.75000 0.60000 NULL HYPOTHESIS: P1 = P2 ALTERNATIVE HYP: P1 <> P2 DIFFERENCE 0.15000 SE (DIFF) 0.07756 Z 1.93 95% CONFIDENCE INTERVAL OF DIFFERENCE LOWER LIMIT -0.00202 UPPER LIMIT 0.30202 A two-tailed test is desired. Find the appropriate p-value for this test of hypothesis. A) p = .0268 B) p = .0536 C) p = .4732 D) p = .0134 439) When blood levels are low at an area hospital, a call goes out to local residents to give blood. The blood center is interested in determining which sex, males or females, is more likely to respond. Random independent samples of 60 females and 100 males produce the following results. A success is defined as a person who responds to the call and donates blood. The computer printout for this analysis appears below: TWO-SAMPLE PROPORTION TEST SAMPLE 1 SAMPLE 2 SAMPLE SIZE 60 100 SUCCESSES 45 60 PROPORTION 0.75000 0.60000 NULL HYPOTHESIS: P1 = P2 ALTERNATIVE HYP: P1 <> P2 DIFFERENCE 0.15000 SE (DIFF) 0.07756 Z 1.93 95% CONFIDENCE INTERVAL OF DIFFERENCE LOWER LIMIT -0.00202 UPPER LIMIT 0.30202 Identify the point estimate for estimating the true difference in the population proportions. A) .30202 B) .07756 C) 1.93 D) .15 73440) When blood levels are low at an area hospital, a call goes out to local residents to give blood. The blood center is interested in determining which sex, males or females, is more likely to respond. Random independent samples of 60 females and 100 males produce the following results. A success is defined as a person who responds to the call and donates blood. The computer printout for this analysis appears below: TWO-SAMPLE PROPORTION TEST SAMPLE 1 SAMPLE 2 SAMPLE SIZE 60 100 SUCCESSES 45 60 PROPORTION 0.75000 0.60000 NULL HYPOTHESIS: P1 = P2 ALTERNATIVE HYP: P1 <> P2 DIFFERENCE 0.15000 SE (DIFF) 0.07756 Z 1.93 95% CONFIDENCE INTERVAL OF DIFFERENCE LOWER LIMIT -0.00202 UPPER LIMIT 0.30202 Use the rejection region approach and ? = .10 to state the correct conclusion for a two-tailed test of hypothesis. A) Reject H 0 . B) Accept H 0 . C) Fail to reject H 0 . D) The correct conclusion cannot be determined with the given information. 74441) When blood levels are low at an area hospital, a call goes out to local residents to give blood. The blood center is interested in determining which sex, males or females, is more likely to respond. Random independent samples of 60 females and 100 males produce the following results. A success is defined as a person who responds to the call and donates blood. The computer printout for this analysis appears below: TWO-SAMPLE PROPORTION TEST SAMPLE 1 SAMPLE 2 SAMPLE SIZE 60 100 SUCCESSES 45 60 PROPORTION 0.75000 0.60000 NULL HYPOTHESIS: P1 = P2 ALTERNATIVE HYP: P1 <> P2 DIFFERENCE 0.15000 SE (DIFF) 0.07756 Z 1.93 95% CONFIDENCE INTERVAL OF DIFFERENCE LOWER LIMIT -0.00202 UPPER LIMIT 0.30202 After this printout was analyzed, one of the directors of the blood bank wanted to go back and take larger samples of both males and females and rework the confidence interval. Based on what you know about confidence intervals, what will happen to the interval width once these larger samples have been taken? (Assume that the level of reliability and the sample proportions did not change once the larger samples were taken). A) The width of the interval could increase or decrease. We just don't know ahead of time. B) The interval will definitely increase in width. C) The interval will definitely decrease in width. 75442) Data were collected from CEO's in the consumer products and telecommunication industries. It is desired to compare the mean salaries between CEO's in the consumer products industry and CEO's in the telecommunications industry. The data were analyzed using the ASP software package. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM SALARY X = Consumer Products Y = Telecommunications SAMPLE MEAN OF X = 1761 SAMPLE VARIANCE OF X = 3.97555E6 SAMPLE SIZE OF X = 21 SAMPLE MEAN OF Y = 1093.5 SAMPLE VARIANCE OF Y = 103255 SAMPLE SIZE OF Y = 21 MEAN X - MEAN Y = 667.5 test statistic = 1.47809 D. F. = 40 P-VALUE = 0.147626 P-VALUE/2 = 0.0738131 SD. ERROR = 451.597 What assumptions are necessary to perform the test above? A) None. The Central Limit Theorem takes care of all assumptions B) Both populations of salaries for the two industries have approximate normal distributions. C) The population of paired differences of salaries is approximately normal. D) The population mean salaries are equal. 76443) Each county in the state of Florida negotiates an annual contract for bread to supply the county's public schools. Sealed bids are submitted by vendors, and the vendor with the lowest bid (price per pound of bread) is selected as the bid winner. Unfortunately, in the early 1980's the suppliers of white bread were found guilty of "price-fixing," i.e., setting the price of bread several cents above the fair, or competitive, price. The data for the 258 sample bid prices were collected independently over six consecutive years. The sample size and mean of the bid prices for each of the six years are reported in the table. Year n Mean 1 40 37.5 2 42 27 3 44 38.9 4 43 41.4 5 45 48.8 6 44 46.5 The attorney theorizes that collusive practices (i.e., price-fixing) occurred during Year 5. One way to test this claim is to compare the mean low bid price during the alleged conspiratory year to the mean during a year when bids were likely to have been competitive. The attorney believes the contracts awarded in Year 1 were competitive and the prices fair. Thus, the low bid price means for Year 1 and Year 5 will be compared. Set up the null and alternative hypothesis for testing whether µ 5 , the true mean low bid price in Year 5, exceeds µ 1 , the true mean in Year 1. A) H 0 : (µ 1 - µ 5 ) = 0 H a : (µ 1 - µ 5 ) ? 0 B) H 0 : (µ 1 - µ 5 ) = 0 H a : (µ 1 - µ 5 ) < 0 C) H 0 : (µ 1 - µ 5 ) = 0 H a : (µ 1 - µ 5 ) > 0 D) H 0 : µ = 0 H a : µ > 0 77444) Each county in the state of Florida negotiates an annual contract for bread to supply the county's public schools. Sealed bids are submitted by vendors, and the vendor with the lowest bid (price per pound of bread) is selected as the bid winner. Unfortunately, in the early 1980's the suppliers of white bread were found guilty of "price-fixing," i.e., setting the price of bread several cents above the fair, or competitive, price. The data for the 204 sample bid prices were collected independently over six consecutive years. The sample size and mean of the bid prices for each of the six years are reported in the table. Year n Mean 1 31 28.5 2 33 18 3 35 29.9 4 34 32.4 5 36 39.8 6 35 37.5 The attorney theorizes that collusive practices (i.e., price-fixing) occurred during Year 5. One way to test this claim is to compare the mean low bid price during the alleged conspiratory year to the mean during a year when bids were likely to have been competitive. The attorney believes the contracts awarded in Year 1 were competitive and the prices fair. Thus, the low bid price means for Year 1 and Year 5 will be compared. A portion of the printout of the hypothesis test follows. Interpret the test results, assuming you select ? = .05. For H a : Mean(lowprice) for year=Y1 -Mean(lowprice) for year=Y5 ? 0 p-value is .009 For H a : Mean(lowprice) for year=Y1 -Mean(lowprice) for year=Y5 < 0 p-value is .002 For H a : Mean(lowprice) for year=Y1 -Mean(lowprice) for year=Y5 > 0 p-value is .998 A) Since the p-value is less than .05, there is insufficient evidence to say that the mean low bid price for Year 5 exceeds the Year 1 mean. B) Since the p-value exceeds .05, there is sufficient evidence to say that the mean low bid price for Year 5 exceeds the Year 1 mean. C) Since the p-value is less than .05, there is sufficient evidence to say that the mean low bid price for Year 5 exceeds the Year 1 mean. D) Since the p-value exceeds .05, there is insufficient evidence to say that the mean low bid price for Year 5 exceeds the Year 1 mean. 78445) Each county in the state of Florida negotiates an annual contract for bread to supply the county's public schools. Sealed bids are submitted by vendors, and the vendor with the lowest bid (price per pound of bread) is selected as the bid winner. Unfortunately, in the early 1980's the suppliers of white bread were found guilty of "price-fixing," i.e., setting the price of bread several cents above the fair, or competitive, price. The data for the 204 sample bid prices were collected independently over six consecutive years. The sample size and mean of the bid prices for each of the six years are reported in the table. Year n Mean 1 31 28.5 2 33 18 3 35 29.9 4 34 32.4 5 36 39.8 6 35 37.5 The attorney theorizes that collusive practices (i.e., price-fixing) occurred during Year 5. One way to test this claim is to compare the mean low bid price during the alleged conspiratory year to the mean during a year when bids were likely to have been competitive. The attorney believes the contracts awarded in Year 1 were competitive and the prices fair. Thus, the low bid price means for Year 1 and Year 5 will be compared. A portion of the printout of the hypothesis test follows. For H a : Mean(lowprice) for year=Y1 -Mean(lowprice) for year=Y5 ? 0 p-value is .006 For H a : Mean(lowprice) for year=Y1 -Mean(lowprice) for year=Y5 < 0 p-value is .003 For H a : Mean(lowprice) for year=Y1 -Mean(lowprice) for year=Y5 > 0 p-value is .998 What must be true to guarantee the validity of the test results? A) The populations of low bid prices in Year 1 and Year 5 both must be normally distributed with identical variances. B) The populations of low bid prices in Year 1 and Year 5 both must be normally distributed with identical means. C) No assumptions are necessary due to the Central Limit Theorem. D) The populations of low bid prices in Year 1 and Year 5 both must be normally distributed. 446) In a controlled laboratory environment, random samples of 10 adults and 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable. The data are summarized below: Sample Mean Sample Variance Adults (1) 77.5° F 4.5 Children (2) 74.5°F 2.5 If the psychologist wished to test the hypothesis that children prefer warmer room temperatures than adults, which set of hypotheses would he use? A) H 0 : (µ 1 - µ 2 ) = 0 vs. H 0 : (µ 1 - µ 2 ) = 0 B) H 0 : (µ 1 - µ 2 ) = 0 vs. H 0 : (µ 1 - µ 2 ) > 0 C) H 0 : (µ 1 - µ 2 ) = 3 vs. H 0 : (µ 1 - µ 2 ) ? 0 D) H 0 : (µ 1 - µ 2 ) = 0 vs. H 0 : (µ 1 - µ 2 ) < 0 79447) In a controlled laboratory environment, random samples of 10 adults and 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable. The data are summarized below: Sample Mean Sample Variance Adults (1) 77.5° F 4.5 Children (2) 74.5°F 2.5 Find the standard error of the estimate for the difference in mean comfortable room temperatures between adults and children. A) 0.7000 B) 1.6279 C) 0.8367 D) 0.1871 448) In a controlled laboratory environment, random samples of 10 adults and 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable. The data are summarized below: Sample Mean Sample Variance Adults (1) 77.5° F 4.5 Children (2) 74.5°F 2.5 Suppose that the psychologist decides to construct a 99% confidence interval for the difference in mean comfortable room temperatures instead of proceeding with a test of hypothesis. The 99% confidence interval turns out to be (-2.9, 3.1). Select the correct statement. A) It cannot be concluded at the 99% confidence level that the true mean comfortable room temperature for children exceeds that for adults. B) It can be concluded at the 99% confidence level that the true mean comfortable room temperature is between 2.9 and 3.1. C) It can be concluded at the 99% confidence level that the true mean room temperature for adults exceeds that for children. D) It cannot be concluded at the 99% confidence level which of the two groups has a larger true mean comfortable room temperature. 449) Consider the following set of data: Men (1) Women (2) Sample Size 100 80 Mean $12,850 $13,000 Standard Deviation $345 $500 To determine if the women have a higher mean salary than the men, we would test: A) H 0 : µ 1 - µ 2 = 0 vs. H a : µ 1 - µ 2 > 0 B) H 0 : µ 1 - µ 2 = 0 vs. H a : µ 1 - µ 2 < 0 C) H 0 : µ 1 - µ 2 = 0 vs. H a : µ 1 - µ 2 = 0 D) H 0 : µ 1 - µ 2 = 0 vs. H a : µ 1 - µ 2 ? 0 80450) Consider the following set of data: Men (1) Women (2) Sample Size 100 80 Mean $12,850 $13,000 Standard Deviation $345 $500 Calculate the appropriate test statistic. A) z = -2.28 B) z = -3.02 C) z = -2.81 D) z = -2.45 451) Consider the following set of data: Men (1) Women (2) Sample Size 100 80 Mean $12,850 $13,000 Standard Deviation $345 $500 Suppose the test statistic turned out to be z = -1.20 (not the correct value). Find a two-tailed p-value for this test statistic. A) p-value = .1151 B) p-value = .3849 C) p-value = .6151 D) p-value = .2302 452) Consider the following set of data: Men (1) Women (2) Sample Size 100 80 Mean $12,850 $13,000 Standard Deviation $345 $500 What assumptions are necessary to perform a test for the difference in population means? A) All of the above are necessary. B) The population has an approximate normal distribution. C) The samples were independently selected. D) The population variances are equal. 81453) Data was collected from CEO's of companies within the consumer products industry sector. The following ASP printout compares the mean return-to-pay ratios between CEO's in the low tech industry with CEO's in the consumer products industry. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM RETURN industry 1 (low tech) (NUMBER = 15) industry 3 (consumer products) (NUMBER = 15) _________________________________________________________ X = industry1 Y = industry3 SAMPLE MEAN OF X = 157.286 SAMPLE VARIANCE OF X = 1563.45 SAMPLE SIZE OF X = 14 SAMPLE MEAN OF Y = 217.583 SAMPLE VARIANCE OF Y = 1601.54 SAMPLE SIZE OF Y = 12 MEAN X - MEAN Y = -60.2976 t = -4.23468 P-VALUE = 0.000290753 P-VALUE/2 = 0.000145377 SD. ERROR = 14.239 Using the printout above, state the alternative hypothesis necessary to test to determine whether a difference exists in the mean return-to-pay ratios between the CEO's in the low tech industry and the CEO's in the consumer products industry. A) H a : µ 1 - µ 2 < 0 B) H a : µ 1 - µ 2 = 0 C) H a : µ 1 - µ 2 ? 0 D) H a : µ 1 - µ 2 > 0 82454) Data was collected from CEO's of companies within the consumer products industry sector. The following ASP printout compares the mean return-to-pay ratios between CEO's in the low tech industry with CEO's in the consumer products industry. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM RETURN industry 1 (low tech) (NUMBER = 15) industry 3 (consumer products) (NUMBER = 15) ___________________________________________________ X = industry1 Y = industry3 SAMPLE MEAN OF X = 157.286 SAMPLE VARIANCE OF X = 1563.45 SAMPLE SIZE OF X = 14 SAMPLE MEAN OF Y = 217.583 SAMPLE VARIANCE OF Y = 1601.54 SAMPLE SIZE OF Y = 12 MEAN X - MEAN Y = -60.2976 t = -4.23468 P-VALUE = 0.000290753 P-VALUE/2 = 0.000145377 SD. ERROR = 14.239 Using the printout above, find the test statistic necessary for testing whether the mean return-to-pay ratio of low tech CEO's exceeds the return-to-pay ratio of consumer product CEO's. A)-4.23468 B)-60.2976 C) 14.239 D) .000145377 83455) Data was collected from CEO's of companies within the consumer products industry sector. The following ASP printout compares the mean return-to-pay ratios between CEO's in the low tech industry with CEO's in the consumer products industry. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM RETURN industry 1 (low tech) (NUMBER = 15) industry 3 (consumer products) (NUMBER = 15) ___________________________________________________ X = industry1 Y = industry3 SAMPLE MEAN OF X = 157.286 SAMPLE VARIANCE OF X = 1563.45 SAMPLE SIZE OF X = 14 SAMPLE MEAN OF Y = 217.583 SAMPLE VARIANCE OF Y = 1601.54 SAMPLE SIZE OF Y = 12 MEAN X - MEAN Y = -60.2976 t = -4.23468 P-VALUE = 0.000290753 P-VALUE/2 = 0.000145377 SD. ERROR = 14.239 Using the printout, which assumption is not necessary for the test above to be valid? A) The population variances are equal. B) Both populations have approximate normal distributions. C) The population means are equal. D) The samples were randomly and independently selected. 84456) Data was collected from CEO's of companies within the consumer products industry sector. The following ASP printout compares the mean return-to-pay ratios between CEO's in the low tech industry with CEO's in the consumer products industry. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM RETURN industry 1 (low tech) (NUMBER = 15) industry 3 (consumer products) (NUMBER = 15) _____________________________________________________________ X = industry1 Y = industry3 SAMPLE MEAN OF X = 157.286 SAMPLE VARIANCE OF X = 1563.45 SAMPLE SIZE OF X = 14 SAMPLE MEAN OF Y = 217.583 SAMPLE VARIANCE OF Y = 1601.54 SAMPLE SIZE OF Y = 12 MEAN X - MEAN Y = -60.2976 t = -4.23468 P-VALUE = 0.000290753 P-VALUE/2 = 0.000145377 SD. ERROR = 14.239 If we conclude that the mean return-to-pay ratios of the consumer products and low tech CEO's are equal when, in fact, a difference really does exist between the means, we would be guilty of making a __________. A) correct decision B) Type III error C) Type II error D) Type I error 85457) A real estate agent gathered data from homes that recently sold in two local neighborhoods. It was decided to test to determine the relationship of the mean land values from the two neighborhoods. The following printout was generated using the individual sample variances as estimates of the unknown population variances. HYPOTHESIS: MEAN X = MEAN Y land_value BROKEN DOWN BY neighborhood X = land value(neighborhood=0) Y = land value(neighborhood=1) SAMPLE MEAN OF X = 14974.5 SAMPLE VARIANCE OF X = 9.91609E6 SAMPLE SIZE OF X = 25 SAMPLE MEAN OF Y = 49443 SAMPLE VARIANCE OF Y = 2.73643E8 SAMPLE SIZE OF Y = 25 MEAN X - MEAN Y = -34468.5 t = -10.2346 D. F. = 48 P-VALUE = 2.00396E-10 P-VALUE/2 = 1.00198E-10 SD. ERROR = 3367.84 State the desired alternative hypothesis to be conducted to determine if neighborhood 1 had a higher mean land value than did neighborhood 0. A) H a : µ 0 - µ 1 > 0 B) H a : µ 0 - µ 1 > 34,468.5 C) H a : µ 0 - µ 1 = 0 D) H a : µ 0 - µ 1 < 0 86458) A real estate agent gathered data from homes that recently sold in two local neighborhoods. It was decided to test to determine the relationship of the mean land values from the two neighborhoods. The following printout was generated using the individual sample variances as estimates of the unknown population variances. HYPOTHESIS: MEAN X = MEAN Y land_value BROKEN DOWN BY neighborhood X = land value(neighborhood=0) Y = land value(neighborhood=1) SAMPLE MEAN OF X = 14974.5 SAMPLE VARIANCE OF X = 9.91609E6 SAMPLE SIZE OF X = 25 SAMPLE MEAN OF Y = 49443 SAMPLE VARIANCE OF Y = 2.73643E8 SAMPLE SIZE OF Y = 25 MEAN X - MEAN Y = -34468.5 t = -10.2346 D. F. = 48 P-VALUE = 2.00396E-10 P-VALUE/2 = 1.00198E-10 SD. ERROR = 3367.84 Which of the following values of ? would lead to a rejection of the null hypothesis? A) ? = .05 B) ? = .025 C) ? = .01 D) All of the above would lead to rejecting H 0 . 87459) A real estate agent gathered data from homes that recently sold in two local neighborhoods. It was decided to test to determine the relationship of the mean land values from the two neighborhoods. The following printout was generated using the individual sample variances as estimates of the unknown population variances. HYPOTHESIS: MEAN X = MEAN Y land_value BROKEN DOWN BY neighborhood X = land value(neighborhood=0) Y = land value(neighborhood=1) SAMPLE MEAN OF X = 14974.5 SAMPLE VARIANCE OF X = 9.91609E6 SAMPLE SIZE OF X = 25 SAMPLE MEAN OF Y = 49443 SAMPLE VARIANCE OF Y = 2.73643E8 SAMPLE SIZE OF Y = 25 MEAN X - MEAN Y = -34468.5 t = -10.2346 D. F. = 48 P-VALUE = 2.00396E-10 P-VALUE/2 = 1.00198E-10 SD. ERROR = 3367.84 State the relationship between µ 0 and µ 1 at the ? = .001 level of reliability. A) µ 0 > µ 1 B) µ 0 < µ 1 C) µ 0 = µ 1 D) µ 0 ? µ 1 88460) A real estate agent gathered data from homes that recently sold in two local neighborhoods. It was decided to test to determine the relationship of the mean land values from the two neighborhoods. The following printout was generated using the individual sample variances as estimates of the unknown population variances. HYPOTHESIS: MEAN X = MEAN Y land_value BROKEN DOWN BY neighborhood X = land value(neighborhood=0) Y = land value(neighborhood=1) SAMPLE MEAN OF X = 14974.5 SAMPLE VARIANCE OF X = 9.91609E6 SAMPLE SIZE OF X = 25 SAMPLE MEAN OF Y = 49443 SAMPLE VARIANCE OF Y = 2.73643E8 SAMPLE SIZE OF Y = 25 MEAN X - MEAN Y = -34468.5 t = -10.2346 D. F. = 48 P-VALUE = 2.00396E-10 P-VALUE/2 = 1.00198E-10 SD. ERROR = 3367.84 What assumptions are necessary for any inferences derived from this printout to be valid? A) The population variances are equal. B) The sample variances are equal. C) The samples were independently selected from approximately normal populations. D) All of the above are necessary. 89461) Data were collected from CEO's in the consumer products and telecommunication industries. It is desired to compare the mean salaries between CEO's in the consumer products industry and CEO's in the telecommunications industry. The data were analyzed using the ASP software package. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM SALARY X = Consumer Products Y = Telecommunications SAMPLE MEAN OF X = 1761 SAMPLE VARIANCE OF X = 3.97555E6 SAMPLE SIZE OF X = 21 SAMPLE MEAN OF Y = 1093.5 SAMPLE VARIANCE OF Y = 103255 SAMPLE SIZE OF Y = 21 MEAN X - MEAN Y = 667.5 test statistic = 1.47809 D. F. = 40 P-VALUE = 0.147626 P-VALUE/2 = 0.0738131 SD. ERROR = 451.597 To determine if the consumer products CEO's have a lower man salary than the telecommunications CEO's, we test: A) H a : µ x - µ y ? 0 B) H a : µ x - µ y < 0 C) H a : µ x - µ y > 0 D) H a : µ x - µ y = 0 90462) Data were collected from CEO's in the consumer products and telecommunication industries. It is desired to compare the mean salaries between CEO's in the consumer products industry and CEO's in the telecommunications industry. The data were analyzed using the ASP software package. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM SALARY X = Consumer Products Y = Telecommunications SAMPLE MEAN OF X = 1761 SAMPLE VARIANCE OF X = 3.97555E6 SAMPLE SIZE OF X = 21 SAMPLE MEAN OF Y = 1093.5 SAMPLE VARIANCE OF Y = 103255 SAMPLE SIZE OF Y = 21 MEAN X - MEAN Y = 667.5 test statistic = 1.47809 D. F. = 40 P-VALUE = 0.147626 P-VALUE/2 = 0.0738131 SD. ERROR = 451.597 Find the p-value for testing a two-tailed alternative hypothesis. A) 0.295252 B) 0.0738131 C) 0.147626 D) 0.9261869 91463) Data were collected from CEO's in the consumer products and telecommunication industries. It is desired to compare the mean salaries between CEO's in the consumer products industry and CEO's in the telecommunications industry. The data were analyzed using the ASP software package. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM SALARY X = Consumer Products Y = Telecommunications SAMPLE MEAN OF X = 1761 SAMPLE VARIANCE OF X = 3.97555E6 SAMPLE SIZE OF X = 21 SAMPLE MEAN OF Y = 1093.5 SAMPLE VARIANCE OF Y = 103255 SAMPLE SIZE OF Y = 21 MEAN X - MEAN Y = 667.5 test statistic = 1.47809 D. F. = 40 P-VALUE = 0.147626 P-VALUE/2 = 0.0738131 SD. ERROR = 451.597 Using ? = .05, give the rejection region for a two-tailed test. A) Reject H 0 if t > 1.684. B) Reject H 0 if t > 1.684 or t < -1.684. C) Reject H 0 if t > 2.021. D) Reject H 0 if t > 2.021 or t < -2.021. 92464) Data were collected from CEO's in the consumer products and telecommunication industries. It is desired to compare the mean salaries between CEO's in the consumer products industry and CEO's in the telecommunications industry. The data were analyzed using the ASP software package. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM SALARY X = Consumer Products Y = Telecommunications SAMPLE MEAN OF X = 1761 SAMPLE VARIANCE OF X = 3.97555E6 SAMPLE SIZE OF X = 21 SAMPLE MEAN OF Y = 1093.5 SAMPLE VARIANCE OF Y = 103255 SAMPLE SIZE OF Y = 21 MEAN X - MEAN Y = 667.5 test statistic = 1.47809 D. F. = 40 P-VALUE = 0.147626 P-VALUE/2 = 0.0738131 SD. ERROR = 451.597 Which of the following assumptions are necessary to perform the test above? A) Both populations of salaries for the two industries have approximate normal distributions. B) The samples were independently collected. C) The population of paired differences of salaries is approximately normal. D) The population mean salaries are equal. 465) The FDA wants to compare the mean caffeine contents of two other brands of 6-oz. cola, Brand A and Brand B. Independent random samples of 6-oz. cans of each brand were selected and the caffeine content of each can determined. The study provided the following summary information. Brand A Brand B Sample size 15 10 Mean (ounces) 18 20 Variance 1.2 1.5 Construct a 99% confidence interval for the true difference between the mean caffeine contents of 6-oz. cans of Brand A and Brand B cola. A)-2 ± (2.807) (s 2 p /15) + ( s 2 p /10), where s 2 p = (14)(1.2) + (9)(1.5) 14 + 9 B) 5 ± (2.58) (s 2 p /15) + ( s 2 p /10), where s 2 p = (14)(1.2) + (9)(1.5) 14 + 9 C)-2 ± (2.807) (1.2/15) + (1.5/10) D)-2 ± (2.58) (1.2/15) + (1.5/10) 93466) The FDA wants to compare the mean caffeine contents of two other brands of 6-oz. cola, Brand A and Brand B. Independent random samples of 6-oz. cans of each brand were selected and the caffeine content of each can determined. The study provided the following summary information. Brand A Brand B Sample size 15 10 Mean (ounces) 18 20 Variance 1.2 1.5 Suppose the above interval is computed to be (-7, 3) (not the true interval, but assume that it is). Interpret this interval practically. A) We are 99% confident that the true mean caffeine content of Brand A, µ 1 , exceeds the true mean caffeine content of Brand B cola, µ 2 . B) Based on the 99% confidence interval, there is no evidence of a difference between the true mean caffeine content of Brand A, µ 1 , and the true mean caffeine content of Brand B cola, µ 2 . C) We are 99% confident that the true mean caffeine content of Brand B cola, µ 2 , exceeds the true mean caffeine content of Brand A, µ 1 . D) We are 99% confident that (x1 - x2), the difference between the sample mean caffeine contents of 6-oz. cans of Brand A and Brand B cola, is included in our interval. 467) The FDA wants to compare the mean caffeine contents of two other brands of 6-oz. cola, Brand A and Brand B. Independent random samples of 6-oz. cans of each brand were selected and the caffeine content of each can determined. The study provided the following summary information. Brand A Brand B Sample size 15 10 Mean (ounces) 18 20 Variance 1.2 1.5 Give the theoretical interpretation of "99% confidence." A) In repeated sampling, 99% of all similarly constructed intervals will enclose the true difference between means (µ 1 - µ 2 ). B) In repeated sampling, (µ 1 - µ 2 ) falls between -7ounces and 3 ounces 99% of the time. C) Theoretically, if 100 intervals were constructed, 99 of the intervals will enclose (x1 - x2), the difference in sample means. D) The probability that 0 falls in our interval is .99. 94468) The FDA wants to compare the mean caffeine contents of two other brands of 6-oz. cola, Brand A and Brand B. Independent random samples of 6-oz. cans of each brand were selected and the caffeine content of each can determined. The study provided the following summary information. Brand A Brand B Sample size 15 10 Mean (ounces) 18 20 Variance 1.2 1.5 What assumptions are necessary for the validity of the interval estimation procedure? A) The errors are independent and normally distributed, with mean 0 and constant variance. B) The populations of caffeine measurements for 6-oz. cans of Brand A and Brand B are normally distributed and have equal variances. C) The populations of caffeine measurements for 6-oz. cans of Brand A and Brand B are normally distributed and have equal means. D) No assumptions are necessary because of the Central Limit Theorem. 469) An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 44 recently hired sales trainees were randomly assigned to one of 11 different "home rooms" - four trainees per room. Each room is identical except for wall color, with 11 different colors used. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to the 11 room colors. At the end of the training program, attitude of each trainee was measured on a 100-pt. scale (the lower the score, the poorer the attitude). The data was subjected to a one-way analysis of variance. How many treatments are in this experiment? A) 100 B) 11 C) 4 D) 55 470) Six different leadership styles (A, B, C, D, E, and F) used by Big-Six accountants were investigated. As part of a designed study, 25 accountants were randomly selected from each of the six leadership style groups (a total of 150 accountants). Each accountant was asked to rate the degree to which their subordinates performed substandard field work on a 100-point scale -- called the "substandard work scale". The objective is to compare the mean substandard work scales of the six leadership styles. The data on substandard work scales for all 150 observations were subjected to an analysis of variance. Identify the type of design employed in this experiment. A) observational design with 150 treatments B) completely randomized design with 6 treatments C) observational design with 6 treatments D) completely randomized design with 150 treatments 471) A certain HMO is attempting to show the benefits of managed health care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that Primary Specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 25 HMO physicians from each of four primary specialties-- General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physician (FP)-- and recorded the total per-member, per-month charges for each. In order to compare the mean charges for the four specialty groups, the data will be subjected to a one-way analysis of variance. Identify the treatments for this group. A) the four specialty groups-- GP, IM, PED, and FP B) the HMO C) the total per-member, per-month charges D) the 100 physicians 95472) A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that Certification Level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 28 physicians from each of the three certification levels-- Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)-- and recorded the total per member per month charges for each (a total of 84 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. How many factors are present in this experiment? A) 84 B) 28 C) 3 D) 1 473) A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that Certification Level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 25 physicians from each of the three certification levels-- Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)-- and recorded the total per-member, per-month charges for each (a total of 75 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. Identify the dependent (response) variable for this experiment. A) the HMO B) the total per-member, per-month charge C) the 75 physicians D) the three certifications groups-- C, E, and I 474) Define the statistical term "Treatments." A) combinations of factor-levels employed in a designed experiment B) experimental units C) correlations among the factors used in an analysis of variance D) assumptions that are satisfied exactly 475) A New Orleans Health Maintenance Organization (HMO) is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that Certification Level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 20 physicians from each of the three certification levels-Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)-and recorded the total per member per month charges for each (a total of 60 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. Identify the treatments for this experiment. A) the total per member per month charge B) the HMO C) the 60 physicians D) the three certification groups-C, E, and I 476) The variable measured in the experiment is called ____________ . A) the treatment B) the factor level C) the response variable D) a sampling unit 477) The variables, quantitative or qualitative, that are related to a response variable are called . A) the factor level B) factors C) the experimental units D) the treatments 478) The intensity of a factor is called _____________. A) the experimental unit B) the treatment C) the design D) a factor level 96479) __________ is a particular combination of levels of the factors involved in an experiment. A) An analysis of variance B) The factor level C) A treatment D) The sampling design 480) Use the appropriate table to find the following F value: F 0.05 , v 1 = 3, v 2 = 28 A) 2.92 B) 3.34 C) 8.62 D) 2.95 481) Find the following: P(F ? 2.16), for v 1 = 5, v 2 = 20 A) 0.95 B) 0.05 C) 0.10 D) 0.90 482) Find the following: P(F > 3.34), for v 1 = 3, v 2 = 14 A) 0.92 B) 0.03 C) 0.05 D) 0.95 483) An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 20 recently hired sales trainees were randomly assigned to one of four different "home rooms" - five trainees per room. Each room is identical except for wall color. The four colors used were light green, light blue, gray and red. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to the four room colors. At the end of the training program, the attitude of each trainee was measured on a 60-pt. scale (the lower the score, the poorer the attitude). The data was subjected to a one-way analysis of variance. ONE-WAY ANOVA FOR ATTITUDE BY COLOR SOURCE DF SS MS F P BETWEEN 3 1678.15 559.3833 59.03782 0.0000 WITHIN 16 151.6 9.475 TOTAL 19 1829.75 SAMPLE GROUP COLOR MEAN SIZE STD DEV Blue 64.300 5 4.3589 Green 64.100 5 3.9623 Gray 45.300 5 1.5811 Red 46.500 5 0.8367 Give the null hypothesis for the ANOVA F test shown on the printout. A) H 0 : p green = p blue = p gray = p red , where the p's represent the proportion with the corresponding attitude B) H 0 : x 1 = x 2 = x 3 = x 4 , where the x's represent the room colors C) H 0 : µ green = µ blue = µ gray = µ red , where the µ's represent mean attitudes for the four rooms D) H 0 : µ 1 = µ 2 = µ 3 = µ 4 = µ 5 , where the µ i represent attitude means for the ith person in each room 97484) An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 20 recently hired sales trainees were randomly assigned to one of four different "home rooms" - five trainees per room. Each room is identical except for wall color. The four colors used were light green, light blue, gray and red. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to the four room colors. At the end of the training program, the attitude of each trainee was measured on a 60-pt. scale (the lower the score, the poorer the attitude). The data was subjected to a one-way analysis of variance. ONE-WAY ANOVA FOR ATTITUDE BY COLOR SOURCE DF SS MS F P BETWEEN 3 1678.15 559.3833 59.03782 0.0000 WITHIN 16 151.6 9.475 TOTAL 19 1829.75 SAMPLE GROUP COLOR MEAN SIZE STD DEV Blue 61.800 5 4.3589 Green 61.600 5 3.9623 Gray 42.800 5 1.5811 Red 44.000 5 0.8367 Fill in the blank. At ? = __________, there is sufficient evidence of differences among the attitude means of sales trainees assigned to the four room colors. A) .05 B) .001 C) .01 D) all of the above 485) Four different leadership styles (A, B, C, and D) used by Big-Six accountants were investigated. As part of a designed study, 15 accountants were randomly selected from each of the four leadership style groups (a total of 60 accountants). Each accountant was asked to rate the degree to which their subordinates performed substandard field work on a 10-point scale -- called the "substandard work scale". The objective is to compare the mean substandard work scales of the four leadership styles. The data on substandard work scales for all 60 observations were subjected to an analysis of variance. ONE-WAY ANOVA FOR SUBSTAND BY STYLE SOURCE DF SS MS F P BETWEEN 3 2931.68 977.225 4.980 0.0039 WITHIN 56 10,988.88 196.230 TOTAL 59 13,920.56 Interpret the results of the ANOVA F test shown on the printout for ? = 0.05. A) At ? =.05, there is insufficient evidence of differences among the substandard work scale means for the four leadership styles. B) At ? = .05, there is sufficient evidence of differences among the substandard work scale means for the four leadership styles. C) At ? =.05, nothing can be said. D) At ? = .05, there is no evidence of interaction. 98486) A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that Certification Level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 22 physicians from each of the three certification levels-- Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)-- and recorded the total per-member, per-month charges for each (a total of 22 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. Write the null hypothesis tested by the ANOVA. A) H 0 : µ C = µ E = µ I = 0 B) H 0 : µ C = µ E = µ I C) H 0 : p 1 = p 2 = p 3 D) H 0 : ß 1 = ß 2 = ß 3 0 487) A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that Certification Level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 21 physicians from each of the three certification levels-- Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)-- and recorded the total per-member, per-month charges for each (a total of 63 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. Give the degrees of freedom appropriate for conducting the ANOVA F-test. A) numerator df = 3, denominator df = 60 B) numerator df = 61, denominator df = 3 C) numerator df = 61, denominator df = 2 D) numerator df = 2, denominator df = 60 488) A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that Certification Level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 20 physicians from each of the three certification levels-- Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)-- and recorded the total per member per month charges for each (a total of 60 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. The results of the ANOVA are summarized in the following table. Take ? = 0.01 Source df SS MS F Value Prob > F Treatments 2 5791.962 2895.981 20.73 .0001 Error 57 7962.9 139.7 Total 59 13,754.862 _____________________________________________________ Interpret the p-value of the ANOVA F test. A) The means of the total per member per month charges for the three groups of physicians differ at ? = .01. B) The model is not statistically useful (at ? = .01) for prediction purposes. C) The means of the total per member per month charges for the three groups of physicians are equal at ? = .01. D) The variances of the total per number per month charges for the three groups of physicians differ at ? = .01. 99489) A company that employs a large number of salespeople is interested in learning which of the salespeople sell the most: those strictly on commission, those with a fixed salary, or those with a reduced fixed salary plus a commission. The previous month's records for a sample of salespeople are inspected and the amount of sales (in dollars) is recorded for each, as shown in the table. Commissioned Fixed Salary Commission Plus Salary $507 $431 $431 $450 $423 $492 $492 $437 $470 $483 $432 $454 $466 $444 $425 Describe the sampling design used to compare the sales amounts for the three compensation systems. 490) A company that employs a large number of salespeople is interested in learning which of the salespeople sell the most: those strictly on commission, those with a fixed salary, or those with a reduced fixed salary plus a commission. The previous month's records for a sample of salespeople are inspected and the amount of sales (in dollars) is recorded for each, as shown in the table. Commissioned Fixed Salary Commission Plus Salary $425 $492 $507 $450 $376 $492 $465 $437 $470 $483 $432 $424 $466 $444 $492 ANALYSIS OF VARIANCE SOURCE FACTOR ERROR TOTAL DF 2 12 14 SS 4195 7945 12140 MS 2097.7 662.1 F 3.17 Test to determine if a difference exists in the mean sale amounts among the three compensation systems. Test using ? = .025. 100491) To be able to provide its clients with comparative information on two large suburban residential communities, a realtor wants to know the average home value in each community. Eight homes are selected at random within each community and are appraised by the realtor. The appraisals are given in the table (in thousands of dollars). Community A 43.5 49.5 67.5 66.5 57.5 32.0 38 71.5 Community B 73.5 36.5 47.5 63.5 44.5 62 68.0 56 General Linear Models Procedure Dependent Variable: PRICE Sum of Mean Source DF Squares Square F Value Pr > F Model 1 40.6406250 40.6406250 0.21 0.6501 Error 14 2648.718750 189.1941964 Corrected Total 15 2689.359375 Is there evidence to suggest that the average home value is different in the two communities? Test using ? = .05. 492) Find the critical value F 0 for a one-tailed test using ? = 0.05, d.f. N = 6, and d.f. D = 16. A) 3.94 B) 2.19 C) 2.74 D) 2.66 493) A partially completed ANOVA table for a completely randomized design is shown here. Source df SS MS F Time 25.2 Error 11 Total 13 86.4 a. Complete the ANOVA table. b. How many treatments are involved in the experiment? c. Do the data provide sufficient evidence to indicate a difference among the population means? Test using ? = .05. 101494) An experiment was conducted to compare the mean iron content in iron ore pieces determined by three different methods: (1) mechanical, (2) manual, and (3) laser. Five 1-meter long pieces of iron ore were removed from a conveyor belt, and the iron content of each piece was determined using each of the three methods. The data are shown below. How should the data be analyzed? Piece Mechanical Manual Laser 1 65.70 66.73 65.67 2 70.80 71.30 71.82 3 65.68 65.74 67.02 4 63.70 63.73 63.57 5 58.56 57.58 59.52 A) randomized block design with three treatments and five blocks B) 3 x 5 factorial design C) completely randomized design with three treatments D) randomized block design with five treatments and three blocks 495) A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. Item A B C 1) paper towels 1.21 1.41 1.36 2) cereal 2.77 3.22 2.97 3) floor cleaner 6.04 5.92 6.93 | | | | | 59) shaving cream 0.98 0.88 0.94 60) canned green beans 0.47 0.62 0.39 Identify the treatments for this experiment. A) the three supermarkets B) the day on which the data were collected C) the 60 x 3 = 180 prices D) the 60 grocery items 496) A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. Item A B C 1) paper towels 1.28 1.48 1.43 2) cereal 2.73 3.18 2.93 3) floor cleaner 6.05 5.93 6.94 | | | | | 59) shaving cream 1.03 0.93 0.99 60) canned green beans 0.43 0.58 0.35 Identify the dependent (response) variable for this experiment. A) the supermarkets B) the prices of the grocery items C) the grocery items D) the mean prices of the grocery items at each supermarket 102497) A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. Item A B C 1) paper towels 1.26 1.46 1.41 2) cereal 2.70 3.15 2.90 3) floor cleaner 6.10 5.98 6.99 | | | | | 59) shaving cream 0.99 0.89 0.95 60) canned green beans 0.44 0.59 0.36 Identify the blocks for this experiment. A) the three supermarkets B) the 60 grocery items C) the 60 x 3 = 180 prices D) the day on which the data were collected 498) A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. Item A B C 1) paper towels 1.21 1.41 1.36 2) cereal 2.74 3.19 2.94 3) floor cleaner 5.93 5.81 6.82 | | | | | 59) shaving cream 0.97 0.87 0.93 60) canned green beans 0.39 0.54 0.31 The results of the ANOVA are summarized in the following table. Source df Anova SS Mean Square F Value Pr > F Supermkt 2 2.6412678 1.3206399 39.23 0.0001 Item 59 215.5949311 3.6541514 108.54 0.0001 Error 118 3.9725322 0.0336655 Corrected Total 179 222.2087311 What is the value of the test statistic for determining whether the three supermarkets have the same average prices? A) 108.54 B) 0.0001 C) 1.3206 D) 39.23 103499) A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. Item A B C 1) paper towels 1.22 1.42 1.37 2) cereal 2.84 3.29 3.04 3) floor cleaner 5.97 5.85 6.86 | | | | | 59) shaving cream 0.90 0.80 0.86 60) canned green beans 0.48 0.63 0.40 The results of the ANOVA are summarized in the following table. Source df Anova SS Mean Square F Value Pr > F Supermkt 2 2.6412678 1.3206399 39.23 0.0001 Item 59 215.5949311 3.6541514 108.54 0.0001 Error 118 3.9725322 0.0336655 Corrected Total 179 222.2087311 Based on the p-value of the test, make the proper conclusion. A) There is sufficient evidence (at ? = .01) to indicate that the mean prices of grocery items at the three supermarkets are identical. B) There is insufficient evidence (at ? = .01) to indicate differences among the mean prices of grocery items at the three supermarkets. C) There is sufficient evidence (at ? = .01) to indicate differences among the mean prices of grocery items at the three supermarkets. D) No conclusions can be drawn from the given information. 500) A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. Item A B C 1) paper towels 1.20 1.40 1.35 2) cereal 2.85 3.30 3.05 3) floor cleaner 6.05 5.93 6.94 | | | | | 59) shaving cream 0.90 0.80 0.86 60) canned green beans 0.47 0.62 0.39 Describe the experiment, including the response variable, factors, and levels. 104501) A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. Item A B C 1) paper towels 1.25 1.45 1.40 2) cereal 2.85 3.30 3.05 3) floor cleaner 6.09 5.97 6.98 | | | | | 59) shaving cream 0.96 0.86 0.92 60) canned green beans 0.48 0.63 0.40 The results of the ANOVA are summarized in the following table. Source df Anova SS Mean Square F Value Pr > F Supermkt 2 2.6412678 1.3206399 39.23 0.0001 Item 59 215.5949311 3.6541514 108.54 0.0001 Error 118 3.9725322 0.0336655 Corrected Total 179 222.2087311 Is there evidence to indicate a difference in the mean prices of the three supermarkets? Test using ? = .01. 502) The lateral drift of a newly constructed skyscraper can be estimated with sophisticated computer software. The goal is to compare the mean drift estimates made by three different computer programs (A, B, and C). Recognizing that lateral drift will depend on building level (floor), the drift (in inches) at each of five levels (Floors 1, 30, 70, 120, and 200) was estimated by each of the three programs: Program Level A B C Floor 1 0.17 0.16 0.18 Floor 30 1.27 1.18 1.19 Floor 70 3.03 2.78 2.75 Floor 120 4.57 4.07 4.02 Floor 200 5.92 4.88 5.94 Explain how to properly analyze this data. A) Chi-square test for randomized block design with five treatments. B) ANOVA F-test for a completely randomized design with three treatments C) ANOVA F-test for interaction in a 5 x 3 factorial design D) ANOVA F-test for a randomized block design with three treatments 105503) An experiment was conducted using a randomized block design. The data from the experiment are displayed in the following table. TREATMENT BLOCK 1 2 3 1 14 19 12 2 13 22 12 3 16 18 13 Fill in the missing entries for an ANOVA table. SOURCE df SS MS F ________________________________________________ Treatments 86.22 Blocks Error ________________________________________________ Total 100.22 504) Suppose an experiment utilizing a random block design has 5 treatments and 9 blocks for a total of 45 observations. Assume that the total Sum of Squares for the response is SS(Total) = 300. If the Sum of Squares for Treatments (SST) is 10% of SS(Total), and the Sum of Squares for Blocks (SSB) is 30% of SS (Total), find the F values for this experiment. A) treatments: F = 1.83; blocks: F = 2.75 B) treatments: F = 1.33; blocks: F = 2.00 C) treatments: F = 1.07; blocks: F = 1.78 D) treatments: F = 12.50; blocks: F = 6.25 505) Suppose a company makes 4 different frozen dinners, and tests their ability to attract customers. They test the frozen dinners in 13 different stores in order to account for any extraneous sources of variation. The company records the number of customers who purchase each product at each store. What assumptions are necessary for the validity of the F statistic for comparing the response means of the 4 frozen dinners? A) None. The Central Limit Theorem eliminates the need for any assumptions. B) The probability distributions of observations corresponding to all the block-treatment combinations are normal. The sampling distributions of the variances of all the block-treatment combinations are normally distributed. C) The means of the observations corresponding to all the block-treatment combinations are equal. The variances of all the probability distributions are equal. D) The probability distributions of observations corresponding to all the block-treatment combinations are normal. The variances of all the probability distributions are equal. 106506) A market research firm is interested in the possible success of new flavors of ice cream. A study was conducted with three different flavors-- peach, almond, and coconut. Three participants were given a sample of each ice cream, in random order, and asked to rate the flavors on a 100-point scale. The results are given in the table below. FLAVOR PARTICIPANT Peach Almond Coconut 1 58 66 56 2 63 81 61 3 66 72 57 a. What is the purpose of blocking on participants in this study? b. Construct an ANOVA summary table using the information given. c. Is there sufficient evidence of a difference in the mean ratings for the three flavors? Use ? = 0.05. Answer the question True or False. 507) When a variable is identified as reducing variation in the response variable, but no additional knowledge concerning the variable is desired, it should be used as the blocking factor in the randomized block design. 508) The randomized block design is an extension of the matched pairs comparison of µ 1 and µ 2 . Solve the problem. 509) A certain HMO is attempting to show the benefits of managed health care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that both Primary Specialty and whether the physician is a foreign or USA medical school graduate are an important factors in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 40 HMO physicians, half foreign graduates and half USA graduates, from each of four primary specialties-- General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physician (FP)-- and recorded the total per-member, per-month charges for each. Thus, information on charges were obtained for a total of n = 160 doctors. The sample mean charges for each of the eight categories are shown in the table. Primary Specialty Foreign Grad USA Grad GP 40.80 43.20 IM 56.30 54.00 PED 20.40 22.20 FP 34.70 38.50 What type of design was used for this experiment? A) 4 x 2 factorial design with 20 replications B) 2 x 2 factorial design with 160 replications C) completely randomized design with two treatments D) completely randomized design with eight treatments 107510) A certain HMO is attempting to show the benefits of managed health care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that both Primary Specialty and whether the physician is a foreign or USA medical school graduate are an important factors in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 40 HMO physicians, half foreign graduates and half USA graduates, from each of four primary specialties-- General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physician (FP)-- and recorded the total per-member, per-month charges for each. Thus, information on charges were obtained for a total of n = 160 doctors. The ANOVA results are summarized in the following table. Source df SS MS F Value Prob > F Specialty 3 22855 7618 60.94 .0001 Medschool 1 105 105 0.84 .6744 Interaction 3 890 297 2.38 .1348 Error 152 18950 125 Total 159 42800 Interpret the test for interaction shown in the ANOVA table. Use ? = 0.01. A) It is impossible to make conclusions about primary specialty and medical school interaction based on the given information. B) There is sufficient evidence at the ? = 0.01 level to say that primary specialty and medical school do not interact. C) There is sufficient evidence at the ? = 0.01 level to say that primary specialty and medical school interact. D) There is insufficient evidence at the ? = 0.01 level to say that primary specialty and medical school interact. 511) A certain HMO is attempting to show the benefits of managed health care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that both Primary Specialty and whether the physician is a foreign or USA medical school graduate are an important factors in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 40 HMO physicians, half foreign graduates and half USA graduates, from each of four primary specialties-- General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physician (FP)-- and recorded the total per-member, per-month charges for each. Thus, information on charges were obtained for a total of n = 160 doctors. The ANOVA results are summarized in the following table. Source df SS MS F Value Prob > F Specialty 3 22855 7618 60.94 .0001 Medschool 1 105 105 0.84 .6744 Interaction 3 890 297 2.38 .1348 Error 152 18950 125 Total 159 42800 Assuming no interaction, is there evidence of a difference between the mean charges of USA and foreign medical school graduates? Use ? = 0.01. A) It is impossible to make conclusions about the main effect of medical school based on the given information B) No, the test for the main effect for medical school is not significant at ? = 0.01. C) No, because the test for the interaction is not significant at ? = 0.01, then the test for the main effect for medical school is not valid. D) Yes, the test for the main effect for medical school is significant at ? = 0.01. 108512) Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been termed the "MUM effect." To investigate the cause of the MUM effect, undergraduates at a certain university participated in an experiment. Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score. (Unknown to the subject, the test taker was a bogus student who was working with the researchers.) The experimenters manipulated two factors, subject visibility and success of test taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success of test taker was either top 20% or bottom 20%. Twenty subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions. Then the time (in seconds) between the end of the test and the delivery of the percentile score from the subject to the test taker was measured. (This variable is called the latency to feedback.) What type of experimental design was employed in this study? A) randomized block design with four treatments and 20 blocks. B) 2 x 2 factorial design with 20 replications. C) completely randomized design with four treatments D) Wilcoxon signed rank design with four treatments 513) Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been termed the "MUM effect." To investigate the cause of the MUM effect, undergraduates at a certain university participated in an experiment. Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score. (Unknown to the subject, the test taker was a bogus student who was working with the researchers.) The experimenters manipulated two factors, subject visibility and success of test taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success of test taker was either top 20% or bottom 20%. Twenty subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions. Then the time (in seconds) between the end of the test and the delivery of the percentile score from the subject to the test taker was measured. (This variable is called the latency to feedback.) In the words of this study, interpret the phrase "Subject visibility and test taker success interact." A) The difference between the mean feedback time for test takers scoring in the top 20% and bottom 20% depends on the visibility of the subject. B) The relationship between feedback time and subject visibility depends on success of the test taker. C) The difference between the mean feedback time for visible and nonvisible subjects depends on the success of the test taker. D) All of the above are correct interpretations. 109514) Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been termed the "MUM effect." To investigate the cause of the MUM effect, 40 undergraduates at a certain university participated in an experiment. Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score. (Unknown to the subject, the test taker was a bogus student who was working with the researchers.) The experimenters manipulated two factors, subject visibility and success of test taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success of test taker was either top 20% or bottom 20%. Ten subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions, then the time (in seconds) between the end of the test and the delivery of the percentile score from the subject to the test taker was measured. (This variable is called the latency to feedback.) The data was subject to an analysis of variance, with the following results: Source df SS MS F PR > F ___________________________________________________________________ Subject visibility 1 1325.16 1325.16 4.09 0.50 Test taker success 1 1380.24 1380.24 4.26 0.046 Visibility x success 1 3385.80 3385.80 10.45 .002 Error 36 11,664.00 324.00 ___________________________________________________________________ Total 39 17,755.20 What conclusions can you draw from the analysis? Use ? = .01. A) At ? = .01, there is sufficient evidence to indicate that subject visibility and test taker success interact. B) At ? = .01, the model is not useful for predicting latency to feedback. C) At ? = .01, there is no evidence of interaction between subject visibility and test taker success. D) At ? = .01, neither subject visibility nor test taker success are important predictors of latency to feedback. 515) The goal of an experiment is to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, we want to determine whether the effect of directional aid (wall signs or map) on travel time depends on starting room location (interior or exterior). Three visitors were assigned to each of the combinations of directional aid and starting room location, and the travel times of each (in seconds) to reach the goal destination room were recorded. DIRECTIONAL AID STARTING Interior ROOM Exterior Wall signs 134 230 121 338 200 136 Map 138 234 126 332 212 138 Explain how to properly analyze these data. A) Chi-square test for a 2 x 2 factorial design B) ANOVA F-test for a randomized block design with two treatments C) ANOVA F-test for a completely randomized design with four treatments D) ANOVA F-test for interaction in a 2 x 2 factorial design with 3 replications 110516) A controlled study was conducted to investigate how two factors-- (1) the level (high or low) of a manager who provides information in a tax audit and (2) when (before or after the audit) this information is received by the auditor-- influence an auditor's evaluation of the evidence obtained from management. Data were collected from 16 managers in each of the four level-timing cells. The response variable recorded is the auditor's assessment of the likelihood of fraudulent information, measured on a 0-100 point scale. One of the objectives of the experiment is to determine whether difference between mean likelihood of fraudulent information for high-level and low-level managers depends on the timing of the information received by the auditor. Explain how to properly analyze these data. A) Conduct an ANOVA F-test for a completely randomized design with four treatments and a sample size of n = 16; follow-up with Bonferroni analysis. B) Conduct an ANOVA F-test for treatments in a randomized block design with two treatments and two blocks; follow-up with Bonferroni analysis. C) Conduct an ANOVA F-test for interaction in a 2 x 2 factorial design with 16 replications. D) Conduct the chi-square test for independence in a two-way contingency table. 517) An appliance manufacturer is interested in determining whether the brand of laundry detergent used affects the average amount of dirt removed from standard household laundry loads. An experiment is set up in which 10 laundry loads are randomly assigned to each of four laundry detergents-- Brands A, B, C, and D. (A total of 40 loads in the experiment.) A manufacturer of Brand A claims that the design of the experiment is flawed. According to the manufacturer, Brand A is better in cold water than in hot water. If all 40 loads in the above experiment were run in hot water, the results will be biased against Brand A. Explain how to redesign the experiment so that the main effects of both laundry detergent brand and temperature of water (hot or cold) on amount of dirt removed, and their possible interaction, can be investigated. A) Use one detergent brand (Brand A). Put 20 loads in hot water and 20 loads in cold water, and compare the results. B) For each of the 40 loads, randomly select one of the detergent brands and randomly select hot or cold water. C) Randomly select two brands (say, A and B) and wash 10 loads in with each brand in cold water. Use hot water in all loads washed by the remaining two brands (say, C and D). D) Consider all eight combinations of Brand and Temperature (e.g., A-hot, A-cold, B-hot, B-cold, etc.). Randomly assign 5 loads to each of the eight combinations. 518) A beverage distributor wanted to determine the combination of advertising agency (two levels) and advertising medium (three levels) that would produce the largest increase in sales per advertising dollar. Each of the advertising agencies prepared ads as required for each of the media-- newspaper, radio, and television. Twelve small towns of roughly the same size were selected for the experiment, and two each were randomly assigned to receive an advertisement prepared and transmitted by each of the six agency-medium combinations. The dollar increases in sales per advertising dollar, based on a 1-month sales period, are shown in the table. Advertising Medium Newspaper Radio Television Agency 1 15.3, 12.7 17.4, 20.1 16.2, 12.7 Agency 2 22.4, 18.9 24.3, 28.8 12.5, 9.4 The SPSS analysis is shown below. _____________________________________________________________________ * * * A N A L Y S I S O F V A R I A N C E * * * SALES BY AGENCY MEDIUM Sum of Mean Signif 111Source of Variation Squares DF Square F of F Main Effects 238.299 3 79.433 13.934 .004 AGENCY 39.967 1 39.967 7.011 .038 MEDIUM 198.332 2 99.166 17.395 .003 AGENCY*MEDIUM 77.345 2 38.672 6.784 .029 Explained 315.644 5 63.129 11.074 .005 Residual 34.205 6 5.701 Total 349.849 11 31.804 (Note: SPSS uses "Explained" instead of "Treatment" in the factorial analysis. Also, SPSS uses "Residual" instead of "Error.") Test to determine if the relationship of the mean dollar increases in sales per advertising dollar for the three advertising mediums depends on the advertising agency selected. Use ? = .05. A) To determine if agency and medium interact, we test: H 0 : Agency and Medium do not interact H a : Agency and Medium do interact. The test statistic is F = 6.784. The p-value for the test is p = .029. Since ? = .05 > p = .029, H 0 is rejected. There is sufficient evidence to indicate that the relationship of the mean dollar increases in sales per advertising dollar for the three advertising mediums depends on the advertising agency selected. 112519) A beverage distributor wanted to determine the combination of advertising agency (two levels) and advertising medium (three levels) that would produce the largest increase in sales per advertising dollar. Each of the advertising agencies prepared ads as required for each of the media-- newspaper, radio, and television. Twelve small towns of roughly the same size were selected for the experiment, and two each were randomly assigned to receive an advertisement prepared and transmitted by each of the six agency-medium combinations. The dollar increases in sales per advertising dollar, based on a 1-month sales period, are shown in the table. Advertising Medium Newspaper Radio Television Agency 1 12.7, 15.3 17.4, 20.1 16.2, 12.7 Agency 2 22.4, 18.9 24.3, 28.8 12.5, 9.4 The SPSS analysis is shown below. _____________________________________________________________________ * * * A N A L Y S I S O F V A R I A N C E * * * SALES BY AGENCY MEDIUM Sum of Mean Signif Source of Variation Squares DF Square F of F Main Effects 238.299 3 79.433 13.934 .004 AGENCY 39.967 1 39.967 7.011 .038 MEDIUM 198.332 2 99.166 17.395 .003 AGENCY*MEDIUM 77.345 2 38.672 6.784 .029 Explained 315.644 5 63.129 11.074 .005 Residual 34.205 6 5.701 Total 349.849 11 31.804 (Note: SPSS uses "Explained" instead of "Treatment" in the factorial analysis. Also, SPSS uses "Residual" instead of "Error.") Would you test the main effects factors, agency and medium, in this example? Explain why or why not. 520) Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been termed the "MUM effect." To investigate the cause of the MUM effect, undergraduates at a certain university participated in an experiment. Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score. (Unknown to the subject, the test taker was a bogus student who was working with the researchers.) The experimenters manipulated two factors, subject visibility and success of test taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success of test taker was either top 20% or bottom 20%. Ten subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions. Then the time (in seconds) between the end of the test and the delivery of the percentile score from the subject to the test taker was measured. (This variable is called the latency to feedback.) Describe the experiment, including the response variable, factors, factor levels, replications, and treatments. 113521) Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been termed the "MUM effect." To investigate the cause of the MUM effect, 40 undergraduates at a certain university participated in an experiment. Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score. (Unknown to the subject, the test taker was a bogus student who was working with the researchers.) The experimenters manipulated two factors, subject visibility and success of test taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success of test taker was either top 20% or bottom 20%. Ten subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions, then the time (in seconds) between the end of the test and the delivery of the percentile score from the subject to the test taker was measured. (This variable is called the latency to feedback.) The data was subject to an analysis of variance, with the following results: Source df SS MS F PR > F ___________________________________________________________________ Subject visibility 1 1325.16 1325.16 4.09 0.50 Test taker success 1 1380.24 1380.24 -1316.81 0.046 Visibility x success 1 3385.80 3385.80 10.45 .002 Error 36 11,664.00 324.00 ___________________________________________________________________ Total 39 17,755.20 Is there evidence to indicate that subject visibility and test taker success interact? Use ? = .01. 522) Complete the ANOVA table. Source df SS MS F _____________________________________________________________________ A 3 216.60 B 1 284.50 AB 527.90 ERROR _____________________________________________________________________ Total 23 7642.80 114523) FACTOR B Level 1 2 3 FACTOR A 1 4.1, 4.1 5.0, 5.2 6.3, 6.1 2 5.6, 5.8 5.3, 5.1 8.8, 9.0 a. Calculate the means. b. The MINITAB ANOVA printout is shown here. Test for interaction at the ? = 0.05 level of significance. Analysis of variance for response. Source df SS MS F __________________________________________________________ A 1 0.53777 0.53777 0.11851 B 2 5.02708 2.51334 0.55391 AB 2 13.49334 6.74667 1.48678 Error 6 27.22667 4.53778 __________________________________________________________ Total 11 46.28486 c. Does the results warrant tests of the two factor mean effects? 115524) Conduct an analysis of variance on the data below. Summarize the results in an ANOVA table. Conduct the appropriate ANOVA F-tests, and interpret the results. Use ? = .05. RACE SEX Caucasian African-American Male 25 31 26 28 25 30 27 29 24 30 Female 27 30 29 31 26 30 26 25 33 29 A) df SS MS F ____________________________________________________ RACE 1 84.05 84.05 46.69 SEX 1 6.05 6.05 3.36 RACE*SEX 1 0.05 0.05 0.03 ERROR 16 28.8 1.8 ____________________________________________________ TOTAL 19 118.95 For the interaction term, F = 0.03 < F .05 = 4.49 (df1 = 2, df2 = 16). We do not reject the null hypothesis of no interaction. There is not significant evidence that race and sex interact. Since the null hypothesis of no interaction was not rejected, we should test the main effects. For sex, F = 3.36 < F .05 = 4.49 (df1 = 2, df2 = 16). We do not reject the null hypothesis of equal means. There is not significant evidence that sex has an effect on the mean response variable. For race, F = 46.691 > F .05 = 4.49 (df1 = 2, df2 = 16). We reject the null hypothesis of equal means. There is significant evidence that race affects the mean response variable. Answer the question True or False. 525) Replication is the term used when more than one item is sampled in each of the a × b cells of a factorial design. 116Solve the problem. 526) A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(y) = ß 0 + ß 1 x, where y-appraised value of the house (in $thousands) and x = number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following results were obtained: y ^ = 74.80 + 24.97x s ß = 71.24, t = 1.05 (for testing ß 0 ) s ß = 2.63, t = 7.49 (for testing ß 1 ) SSE = 60,775, MSE = 841, s = 29, r 2 = .44 Range of the x-values: 5 - 11 Range of the y-values: 160 - 300 Give a practical interpretation of the estimate of the slope of the least squares line. A) For each additional dollar of appraised value, we estimate the number of rooms in the house to increase by 24.97 rooms. B) For each additional room in the house, we estimate the appraised value to increase $74,800. C) For each additional room in the house, we estimate the appraised value to increase $24,970. D) For a house with 0 rooms, we estimate the appraised value to be $74,800. 527) Is there a relationship between the raises administrators at State University receive and their performance on the job? A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the straight-line regression model E(y) = ß 0 + ß 1 x. Using the method of least squares, the faculty group obtained the following prediction equation: y ^ = 14,000 - 2,000x Interpret the estimated slope of the line. A) For a $1 increase in an administrator's raise, we estimate the administrator's rating to decrease 2,000 points. B) For an administrator with a rating of 1.0, we estimate his/her raise to be $2,000. C) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to decrease $2,000. D) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $2,000. 528) State the four basic assumptions about the general form of the probability distribution of the random error ?. 117529) Is there a relationship between the raises administrators at State University receive and their performance on the job? A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the straight-line regression model E(y) = ß 0 + ß 1 x. Using the method of least squares, the faculty group obtained the following prediction equation: y ^ = 14,000 - 2,000x Interpret the estimated y-intercept of the line. A) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $14,000. B) For an administrator who receives a rating of zero, we estimate his or her raise to be $14,000. C) There is no practical interpretation, since rating of 0 is nonsensical and outside the range of the sample data. D) The base administrator raise at State University is $14,000. 530) In a comprehensive road test on all new car models, one variable measured is the time it takes a car to accelerate from 0 to 60 miles per hour. To model acceleration time, a regression analysis is conducted on a random sample of 129 new cars. TIME60: y = Elapsed time (in seconds) from 0 mph to 60 mph MAX: x 1 = Maximum speed attained (miles per hour) Initially, the simple linear model E(y) = ß 0 + ß 1 x 1 was fit to the data. Computer printouts for the analysis are given below: NWEIGHTED LEAST SQUARES LINEAR REGRESSION OF TIME60 PREDICTOR VARIABLES COEFFICIENT STD ERROR STUDENT'S T P CONSTANT 18.7171 0.63708 29.38 0.0000 MAX -0.08365 0.00491 -17.05 0.0000 R-SQUARED 0.6960 RESID. MEAN SQUARE (MSE) 1.28695 ADJUSTED R-SQUARED 0.6937 STANDARD DEVIATION 1.13444 SOURCE DF SS MS F P REGRESSION 1 374.285 374.285 290.83 0.0000 RESIDUAL 127 163.443 1.28695 TOTAL 128 537.728 CASES INCLUDED 129 MISSING CASES 0 Find and interpret the estimate ß ^ 1 in the printout above. 118531) The data in the table are typical prices for a gallon of regular leaded gasoline and a barrel of crude oil for the indicated years. Year Gasoline y(¢ per gallon) Crude Oil ($ per barrel) Year Gasoline y(¢ per gallon) Crude Oil ($ per barrel) 1975 57 10.38 1983 116 28.99 1976 59 10.89 1984 113 28.63 1977 62 11.96 1985 112 36.75 1978 63 12.46 1986 86 14.55 1979 86 17.72 1987 90 17.90 1980 119 28.07 1988 90 14.67 1981 131 35.24 1989 100 17.97 1982 122 31.87 1990 115 22.23 Summary statistics yield: SS xx = 1222.2771, SS xy = 3031.7125, SS yy = 9144.9375, x = 21.2675, and y = 95.0625. Find the least squares line that uses crude oil price to predict gasoline price. 532) In a study of feeding behavior, zoologists recorded the number of grunts of a warthog feeding by a lake in the 15 minute period following the addition of food. The data showing the weekly number of grunts and and the age of the warthog (in days) are listed below: Week Number of Grunts Age (days) 1 86 121 2 64 137 3 35 151 4 40 156 5 59 163 6 36 170 7 58 179 8 13 185 9 16 191 a. Write the equation of a straight-line model relating number of grunts (y) to age (x). b. Give the least squares prediction equation. c. Give a practical interpretation of the value of ß ^ 0, if possible. d. Give a practical interpretation of the value of ß ^ 1, if possible. 119533) In a comprehensive road test on all new car models, one variable measured is the time it takes a car to accelerate from 0 to 60 miles per hour. To model acceleration time, a regression analysis is conducted on a random sample of 129 new cars. TIME60: y = Elapsed time (in seconds) from 0 mph to 60 mph MAX: x 1 = Maximum speed attained (miles per hour) Initially, the simple linear model E(y) = ß 0 + ß 1x1 was fit to the data. Computer printouts for the analysis are given below: NWEIGHTED LEAST SQUARES LINEAR REGRESSION OF TIME60 PREDICTOR VARIABLES COEFFICIENT STD ERROR STUDENT'S T P CONSTANT 18.7171 0.63708 29.38 0.0000 MAX -0.08365 0.00491 -17.05 0.0000 R-SQUARED 0.6960 RESID. MEAN SQUARE (MSE) 1.28695 ADJUSTED R-SQUARED 0.6937 STANDARD DEVIATION 1.13444 SOURCE DF SS MS F P REGRESSION 1 374.285 374.285 290.83 0.0000 RESIDUAL 127 163.443 1.28695 TOTAL 128 537.728 CASES INCLUDED 129 MISSING CASES 0 Fill in the blank: "At ? =.05, there is ________________ between maximum speed and acceleration time." A) insufficient evidence of a negative linear relationship B) sufficient evidence of a positive linear relationship C) sufficient evidence of a negative linear relationship D) insufficient evidence of a linear relationship 120534) A manufacturer of boiler drums wants to use regression to predict the number of man-hours needed to erect drums in the future. The manufacturer collected a random sample of 35 boilers and measured the following two variables: MANHRS: y = Number of man-hours required to erect the drum PRESSURE: x 1 = Boiler design pressure (pounds per square inch, i.e., psi) Initially, the simple linear model E(y) = ß 1 + ß 1x1 was fit to the data. A printout for the analysis appears below: UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF MANHRS PREDICTOR VARIABLES COEFFICIENT STD ERROR STUDENT'S T P CONSTANT 1.88059 0.58380 3.22 0.0028 PRESSURE 0.00321 0.00163 2.17 0.0300 R-SQUARED 0.4342 RESID. MEAN SQUARE (MSE) 4.25460 ADJUSTED R-SQUARED 0.4176 STANDARD DEVIATION 2.06267 SOURCE DF SS MS F P REGRESSION 1 111.008 111.008 5.19 0.0300 RESIDUAL 34 144.656 4.25160 TOTAL 35 255.665 Fill in the blank. At ? =.01, there is ____________ between man-hours and pressure. A) insufficient evidence of a positive linear relationship B) sufficient evidence of a linear relationship C) sufficient evidence of a negative linear relationship D) sufficient evidence of a positive linear relationship 121535) A manufacturer of boiler drums wants to use regression to predict the number of man-hours needed to erect drums in the future. The manufacturer collected a random sample of 35 boilers and measured the following two variables: MANHRS: y = Number of man-hours required to erect the drum PRESSURE: x 1 = Boiler design pressure (pounds per square inch, i.e., psi) Initially, the simple linear model E(y) = ß 1 + ß 1x1 was fit to the data. A printout for the analysis appears below: UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF MANHRS PREDICTOR VARIABLES COEFFICIENT STD ERROR STUDENT'S T P CONSTANT 1.88059 0.58380 3.22 0.0028 PRESSURE 0.00321 0.00163 2.17 0.0300 R-SQUARED 0.4342 RESID. MEAN SQUARE (MSE) 4.25460 ADJUSTED R-SQUARED 0.4176 STANDARD DEVIATION 2.06267 SOURCE DF SS MS F P REGRESSION 1 111.008 111.008 5.19 0.0300 RESIDUAL 34 144.656 4.25160 TOTAL 35 255.665 Give a practical interpretation of the estimated slope of the least squares line. A) We estimate the number of man-hours to increase .003 hour when pressure increases by 1 pound per square inch. B) About .3% of the sample variation in number of man-hours can be explained by the simple linear model. C) Approx. 95% of the actual man-hours required to build a drum will fall within .006 hour of their predicted values. D) We estimate the pressure to increase .003 pound per square inch when number of man-hours increases by 1. 122536) A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(y) = ß 0 + ß 1 x, where y = appraised value of the house (in $thousands) and x = number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following results were obtained: y ^ = 74.80 + 19.72x s ß = 71.24, t = 1.05 (for testing ß 0 ) s ß = 2.63, t = 7.49 (for testing ß 1 ) SSE = 60,775, MSE = 841, s = 29, r 2 = .44 Range of the x-values: 5 - 11 Range of the y-values: 160 - 300 What set of hypotheses would you test to determine whether appraised value is positively linearly related to number of rooms? A) H 0 : ß 1 = 19.72 vs. H a : ß 1 > 19.72 B) H 0 : ß 1 = 0 vs. H a : ß 1 ? 0 C) H 0 : ß 1 = 0 vs. H a : ß 1 > 0 D) H 0 : ß 1 = 0 vs. H a : ß 1 < 0 537) A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (y), measured in dollars per month, for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue (x), measured in $ million. Data for 21 companies who use the bank's services were used to fit the model E(y) = ß 0 + ß 1 x. The results of the simple linear regression are provided below. _____________________________________________________________________ y ^ = 2,700 + 20x, s = 65, 2-tailed p-value = .064 (for testing ß 1 ) Interpret the p-value for testing whether ß 1 exceeds 0. A) There is insufficient evidence (at ? = .05) to conclude that sales revenue (x) is positively linearly related to service charge (y). B) For every $1 million increase in sales revenue (x), we expect a service charge (y) to increase $.064. C) Sales revenue (x) is a lousy predictor of service charge (y). D) There is sufficient evidence (at ? = .05) to conclude that sales revenue (x) is positively linearly related to service charge (y). 123538) A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (y), measured in dollars per month, for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue (x), measured in $ million. Data for 21 companies who use the bank's services were used to fit the model E(y) = ß 0 + ß 1 x. Suppose a 95% confidence interval for ß 1 is (15, 25). Interpret the interval. A) We are 95% confident that sales revenue (x) will increase between $15 and $25 million for every $1 increase in service charge (y). B) We are 95% confident that the mean service charge will fall between $15 and $25 per month. C) We are 95% confident that service charge (y) will increase between $15 and $25 for every $1 million increase in sales revenue (x). D) We are 95% confident that service charge (y) will decrease between $15 and $25 for every $1 million increase in sales revenue (x). 539) The dean of the Business School at a small Florida college wishes to determine whether the grade-point average (GPA) of a graduating student can be used to predict the graduate's starting salary. More specifically, the dean wants to know whether higher GPA's lead to higher starting salaries. Records for 23 of last year's Business School graduates are selected at random, and data on GPA (x) and starting salary (y, in $thousands) for each graduate were used to fit the model E(y) = ß 0 + ß 1 x. The results of the simple linear regression are provided below. y ^ = 4.25 + 2.75x, SSxy = 5.15, SSxx = 1.87 SSyy = 15.17, SSE = 1.0075 Range of the x-values: 2.23 - 3.85 Range of the y-values: 9.3 - 15.6 The value of the test statistic for testing ß 1 is 17.169. Make the proper conclusion. A) At any reasonable ?, there is no relationship between GPA and starting salary. B) There is sufficient evidence (at ? = .05) to conclude that GPA is positively linearly related to starting salary. C) There is insufficient evidence (at ? = .10) to conclude that GPA is a useful linear predictor of starting salary. D) There is insufficient evidence (at ? = .05) to conclude that GPA is positively linearly related to starting salary. 124540) Consider the following model y = ß 0 + ß 1 x + ?, where y is the daily rate of return of a stock, and x is the daily rate of return of the stock market as a whole, measured by the daily rate of return of Standard & Poor's (S&P) 500 Composite Index. Using a random sample of n = 12 days from 1980, the least squares lines shown in the table below were obtained for four firms. The estimated standard error of ß ^ 1 is shown to the right of each least squares prediction equation. Firm Estimated Market Model Estimated Standard Error of ß 1 Company A y = .0010 + 1.40x .03 Company B y = .0005 - 1.21x .06 Company C y = .0010 + 1.62x 1.34 Company D y = .0013 + .76x .15 Calculate the test statistic for determining whether the market model is useful for predicting daily rate of return of Company A's stock. A) 46.7 B) 161.6 C) 1.40 D) 1.40 ± .067 541) Consider the following model y = ß 0 + ß 1 x + ?, where y is the daily rate of return of a stock, and x is the daily rate of return of the stock market as a whole, measured by the daily rate of return of Standard & Poor's (S&P) 500 Composite Index. Using a random sample of n = 12 days from 1980, the least squares lines shown in the table below were obtained for four firms. The estimated standard error of ß ^ 1 is shown to the right of each least squares prediction equation. Firm Estimated Market Model Estimated Standard Error of ß 1 Company A y = .0010 + 1.40x .03 Company B y = .0005 - 1.21x .06 Company C y = .0010 + 1.62x 1.34 Company D y = .0013 + .76x .15 For which of the three stocks, Companies B, C, or D, is there evidence (at ? = .05) of a positive linear relationship between y and x? A) Companies B and C only B) Company C only C) Companies B and D only D) Company D only 125(Situation P) Each year U.S. News & World Report conducts its "Survey of America's Best Graduate and Professional Schools." The top 25 business schools in 1991, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table. For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. School GMAT Acc. Rate Salary 1. Harvard 644 15.0% $ 63,000 2. Stanford 665 10.2 60,000 3. Penn 644 19.4 55,000 4. Northwestern 640 22.6 54,000 5. MIT 650 21.3 57,000 6. Chicago 632 30.0 55,269 7. Duke 630 18.2 53,300 8. Dartmouth 649 13.4 52,000 9. Virginia 630 23.0 55,269 10. Michigan 620 32.4 53.300 11. Columbia 635 37.1 52,000 12. Cornell 648 14.9 50,700 13. CMU 630 31.2 52,050 14. UNC 625 15.4 50,800 15. Cal-Berkeley 634 24.7 50,000 16. UCLA 640 20.7 51,494 17. Texas 612 28.1 43,985 18. Indiana 600 29.0 44,119 19. NYU 610 35.0 53,161 20. Purdue 595 26.8 43,500 21. USC 610 31.9 49,080 22. Pittsburgh 605 33.0 43,500 23. Georgetown 617 31.7 45,156 24. Maryland 593 28.1 42,925 25. Rochester 605 35.9 44,499 The academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using the 25 data points in the table are shown below. ----------------------------------------------------------------------- ß 0 = -92040 ß ^ 1 = 228 s = 3213 R 2 = .66 r = .81 df = 23 t = 6.67 ----------------------------------------------------------------------- 542) For the situation above, write the equation of the probabilistic model of interest. A) Salary = ß 0 + ß 1 (GMAT) + ? B) Salary = ß 0 + ß 1 (GMAT) C) GMAT = ß 0 + ß 1 (SALARY) D) GMAT = ß 0 + ß 1 (SALARY) + ? 543) For the situation above, write the equation of the least squares line. A) SALARY = 228 + 92040 (GMAT) B) SALARY = -92040 + 228 (GMAT) C) GMAT = 228 - 92040 (SALARY) D) GMAT = -92040 + 228 (SALARY) 126544) For the situation above, give a practical interpretation of ß ^ 0 = -92040. A) The value has no practical interpretation since a GMAT of 0 is nonsensical and outside the range of the sample data. B) We estimate the base SALARY of graduates of a top business school to be $ -92,040. C) We expect to predict SALARY to within 2(92040) = $184,080 of its true value using GMAT in a straight-line model. D) We estimate SALARY to decrease $92,040 for every 1-point increase in GMAT. 545) For the situation above, give a practical interpretation of ß ^ 1 = 228. A) We estimate SALARY to increase $228 for every 1-point increase in GMAT. B) The value has no practical interpretation since a GMAT of 0 is nonsensical and outside the range of the sample data. C) We expect to predict SALARY to within 2(228) = $456 of its true value using GMAT in a straight-line model. D) We estimate GMAT to increase 228 points for every $1 increase in SALARY. 546) For the situation above, give a practical interpretation of s = 3213. A) We expect to predict SALARY to within 2(3213) = $6,426 of its true value using GMAT in a straight-line model. B) Our predicted value of SALARY will equal 2(3213) = $6,426 for any value of GMAT. C) We estimate SALARY to increase $3,213 for every 1-point increase in GMAT. D) We expect the predicted SALARY to deviate from actual SALARY by at least 2(3213) = $6,426 using GMAT in a straight-line model. 547) For the situation above, give a practical interpretation of R 2 = .66. A) We can predict SALARY correctly 66% of the time using GMAT in a straight-line model. B) We estimate SALARY to increase $.66 for every 1-point increase in GMAT. C) We expect to predict SALARY to within 2( .66) = $1,620 of its true value using GMAT in a straight-line model. D) 66% of the sample variation in SALARY can be explained by using GMAT in a straight-line model. 548) For the situation above, give a practical interpretation of r = .81. A) There appears to be a positive correlation between SALARY and GMAT. B) We can predict SALARY correctly 81% of the time using GMAT in a straight-line model. C) 81% of the sample variation in SALARY can be explained by using GMAT in a straight-line model. D) We estimate SALARY to increase 81% for every 1-point increase in GMAT. 549) Set up the null and alternative hypotheses for testing whether a positive linear relationship exists between SALARY and GMAT in the situation above. A) H 0 : ß 1 = 0 vs. H a : ß 1 > 0 B) H 0 : ß 1 > 0 vs. H a : ß 1 < 0 C) H 0 : ß 1 = 228 vs. H a : ß 1 > 228 D) H 0 : ß 1 = 0 vs. H a : ß 1 ? 0 550) For the situation above, give a practical interpretation of t = 6.67. A) There is evidence (at ? = .05) of at least a positive linear relationship between SALARY and GMAT. B) There is evidence (at ? = .05) to indicate that ß 1 = 0. C) Only 6.67% of the sample variation in SALARY can be explained by using GMAT in a straight-line model. D) We estimate SALARY to increase $6.67 for every 1-point increase in GMAT. 127551) A 95% prediction interval for SALARY when GMAT = 600 is ($37,915, $51,948). Interpret this interval for the situation above. A) We are 95% confident that the SALARY of a top business school graduate with a GMAT of 600 will fall between $37,915 and $51,984. B) We are 95% confident that the SALARY of a top business school graduate will fall between $37,915 and $51,984. C) We are 95% confident that the mean SALARY of all top business school graduates with GMATs of 600 will fall between $37,915 and $51,984. D) We are 95% confident that the increase in SALARY for a 600-point increase in GMAT will fall between $37,915 and $51,984. 552) For the situation above, which of the following is not an assumption required for the simple linear regression analysis to be valid? A) The errors of predicting SALARY have a variance that is constant for any given value of GMAT. B) SALARY is independent of GMAT. C) The errors of predicting SALARY have a mean of 0. D) The errors of predicting SALARY are normally distributed. Solve the problem. 553) As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): x 1 = average high school grade in mathematics (HSM) x 2 = average high school grade in science (HSS) x 3 = average high school grade in English (HSE) x 4 = SAT mathematics score (SATM) x 4 = SAT verbal score (SATV) The first-order model below was fit to data with the following results: E(y) = ß 0 + ß 1 x 1 + ß 2 x 2 + ß 3 x 3 + ß 4 x 4 + ß 5 x 5 _____________________________________________________________________ SOURCE DF SS MS F VALUE PROB > F MODEL 5 28.64 5.73 11.69 .0001 ERROR 218 106.82 0.49 TOTAL 223 135.46 ROOT MSE 0.700 R-SQUARE 0.211 DEP MEAN 4.635 ADJ R-SQ 0.193 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T FOR 0: PARAMETER = 0 PROB > |T| INTERCEPT 2.327 0.039 5.817 0.0001 X1 (HSM) 0.146 0.037 3.718 0.0003 X2 (HSS) 0.036 0.038 0.950 0.3432 X3 (HSE) 0.055 0.040 1.397 0.1637 X4 (SATM) 0.00094 0.00068 1.376 0.1702 X5 (SATV) -0.00041 0.00059 -0.689 0.4915 128A 95% confidence interval for ß 1 is (.06, .22). Interpret this result. A) We are 95% confident that the mean GPA of all CS freshmen falls between .06 and .22. B) We are 95% confident that a CS freshman's GPA increases by an amount between .06 and .22 point for every 1-point increase in average HS math grade, holding x 2 - x 5 constant. C) We are 95% confident that a CS freshman's HS math grade increases by an amount between .06 and .22 point for every 1-point increase in GPA, holding x 2 - x 5 constant. D) 95% of the GPAs fall within .06 to .22 of their true values. 554) As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): x 1 = average high school grade in mathematics (HSM) x 2 = average high school grade in science (HSS) x 3 = average high school grade in English (HSE) x 4 = SAT mathematics score (SATM) x 4 = SAT verbal score (SATV) The first-order model below was fit to data with the following results: E(y) = ß 0 + ß 1 x 1 + ß 2 x 2 + ß 3 x 3 + ß 4 x 4 + ß 5 x 5 _____________________________________________________________________ SOURCE DF SS MS F VALUE PROB > F MODEL 5 28.64 5.73 11.69 .0001 ERROR 218 106.82 0.49 TOTAL 223 135.46 ROOT MSE 0.700 R-SQUARE 0.211 DEP MEAN 4.635 ADJ R-SQ 0.193 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T FOR 0: PARAMETER = 0 PROB > |T| INTERCEPT 2.327 0.039 5.817 0.0001 X1 (HSM) 0.146 0.037 3.718 0.0003 X2 (HSS) 0.036 0.038 0.950 0.3432 X3 (HSE) 0.055 0.040 1.397 0.1637 X4 (SATM) 0.00094 0.00068 1.376 0.1702 X5 (SATV) -0.00041 0.00059 -0.689 0.4915 What is the correct interpretation of R 2 , the coefficient of determination of the model? A) Approximately 79% of the sample variation in GPAs can be explained by the first-order model. B) We expect to predict GPA to within approximately .21 point of its true value. C) We are 79% confident that the model is useful for predicting y. D) Approximately 21% of the sample variation in GPAs can be explained by the first-order model. 129555) As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): x 1 = average high school grade in mathematics (HSM) x 2 = average high school grade in science (HSS) x 3 = average high school grade in English (HSE) x 4 = SAT mathematics score (SATM) x 4 = SAT verbal score (SATV) The first-order model below was fit to data with the following results: E(y) = ß 0 + ß 1 x 1 + ß 2 x 2 + ß 3 x 3 + ß 4 x 4 + ß 5 x 5 _____________________________________________________________________ SOURCE DF SS MS F VALUE PROB > F MODEL 5 28.64 5.73 11.69 .0001 ERROR 218 106.82 0.49 TOTAL 223 135.46 ROOT MSE 0.700 R-SQUARE 0.211 DEP MEAN 4.635 ADJ R-SQ 0.193 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T FOR 0: PARAMETER = 0 PROB > |T| INTERCEPT 2.327 0.039 5.817 0.0001 X1 (HSM) 0.146 0.037 3.718 0.0003 X2 (HSS) 0.036 0.038 0.950 0.3432 X3 (HSE) 0.055 0.040 1.397 0.1637 X4 (SATM) 0.00094 0.00068 1.376 0.1702 X5 (SATV) -0.00041 0.00059 -0.689 0.4915 Give the null hypothesis for testing the overall adequacy of the model. A) H 0 : ß 0 = ß 1 = ß 2 = ß 3 = ß 4 = ß 5 = 0 B) H 0 : ß 1 = 0 C) H 0 : ß 0 + ß 1 x 1 + ß 2 x 2 + ß 3 x 3 + ß 4 x 4 + ß 5 x 5 = 0 D) H 0 : ß 1 = ß 2 = ß 3 = ß 4 = ß 5 = 0 556) As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): x 1 = average high school grade in mathematics (HSM) x 2 = average high school grade in science (HSS) x 3 = average high school grade in English (HSE) x 4 = SAT mathematics score (SATM) x 4 = SAT verbal score (SATV) The first-order model below was fit to data with the following results: E(y) = ß 0 + ß 1 x 1 + ß 2 x 2 + ß 3 x 3 + ß 4 x 4 + ß 5 x 5 130_____________________________________________________________________ SOURCE DF SS MS F VALUE PROB > F MODEL 5 28.64 5.73 11.69 .0001 ERROR 218 106.82 0.49 TOTAL 223 135.46 ROOT MSE 0.700 R-SQUARE 0.211 DEP MEAN 4.635 ADJ R-SQ 0.193 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T FOR 0: PARAMETER = 0 PROB > |T| INTERCEPT 2.327 0.039 5.817 0.0001 X1 (HSM) 0.146 0.037 3.718 0.0003 X2 (HSS) 0.036 0.038 0.950 0.3432 X3 (HSE) 0.055 0.040 1.397 0.1637 X4 (SATM) 0.00094 0.00068 1.376 0.1702 X5 (SATV) -0.00041 0.00059 -0.689 0.4915 Interpret the value under PROB > F. A) Over 99% of the variation in GPAs can be explained by the model. B) Accept H 0 (at ? = .01); at least one of the ß-coefficients in the first-order model is equal to 0. C) There is sufficient evidence (at ? = .01) to conclude that the first-order model is statistically useful for predicting GPA. D) There is insufficient evidence (at ? = .01) to conclude that the first-order model is statistically useful for predicting GPA. 131557) What factors affect the sale price of oceanside condominium units? To answer this question, the following data were recorded for each of the n = 105 units sold at auction: y = Sale price ($thousands) x 1 = Floor height (1, 2, 3, ... , 8) x 2 = 1 if ocean view, 0 if bay view The first-order model below was fit to the data with the following results: E(y) = ß 0 + ß 1 x 1 + ß 2 x 2 _____________________________________________________________________ SOURCE DF SS MS F VALUE PROB > F MODEL 2 19.08 8.04 4.14 .0250 ERROR 102 197.96 1.94 TOTAL 104 217.04 ROOT MSE 1.393 R-SQUARE .088 VARIABLES PARAMETER ESTIMATE STANDARD ERROR T FOR 0: PARAMETER = 0 PROB > |T| INTERCEPT 17.770 .416 42.71 .0001 X 1 -.073 .053 -1.39 .1674 X 2 3.137 .222 14.08 .0001 What is the correct interpretation of the coefficient of determination of the model? (Recall y is recorded in thousands of dollars.) A) Approximately 2.5% of the sample variation in sale prices can be explained by the first-order model. B) We are 91.2% confident that the model is useful for predicting y. C) Approximately 8.8% of the sample variation in sale prices can be explained by the first-order model. D) We expect to predict sale price to within approximately $2,786 of its true value. 132558) What factors affect the sale price of oceanside condominium units? To answer this question, the following data were recorded for each of the n = 105 units sold at auction: y = Sale price ($thousands) x 1 = Floor height (1, 2, 3, ... , 8) x 2 = 1 if ocean view, 0 if bay view The first-order model below was fit to the data with the following results: E(y) = ß 0 + ß 1 x 1 + ß 2 x 2 _____________________________________________________________________ SOURCE DF SS MS F VALUE PROB > F MODEL 2 19.08 8.04 4.14 .0250 ERROR 102 197.96 1.94 TOTAL 104 217.04 ROOT MSE 1.393 R-SQUARE .088 VARIABLES PARAMETER ESTIMATE STANDARD ERROR T FOR 0: PARAMETER = 0 PROB > |T| INTERCEPT 17.770 .416 42.71 .0001 X -.073 .053 -1.39 .1674 X · X 3.137 .222 14.08 .0001 Interpret the value under PROB > F. A) There is sufficient evidence (at ? = .05) to conclude that the first-order model is statistically useful for predicting sale price. B) About 91% of the sample variation in sale prices can be explained by the first-order model. C) There is insufficient evidence (at ? = .05) to conclude that the first-order model is statistically useful for predicting sale price. D) We are 2.5% confident that at least one of the ß-coefficients in the first-order model is not equal to 0. 559) During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first three tests. To test this claim, multiple regression will be used to model Test4 score (y), as a function of Test1 score ( x 1 ), Test 2 score (x 2 ), and Test3 score (x 3 ). [Note: All test scores range from 200 to 800, with higher scores indicative of a higher quality product.] Consider the model: E(y) = ß 1 + ß 1 x 1 + ß 2 x 2 + ß 3 x 3 The global F statistic is used to test the null hypothesis, H 0 : ß 1 = ß 2 = ß 3 = 0. Describe this hypothesis in words. A) The first three test scores are useful predictors of Test4 score. B) The model is not statistically useful for predicting Test4 score. C) The first three test scores are lousy predictors of Test4 score. D) The model is statistically useful for predicting Test4 score. 133560) Retail price data for n = 60 hard disk drives were recently extracted from a computer magazine. Three of the many variables recorded for each hard disk drive were: y = Retail PRICE (measured in dollars) x 1 = Microprocessor SPEED (measured in megahertz) (Values in sample range from 10 to 40) x 2 = CHIP size (measured in computer processing units) (Values in sample range from 286 to 486) The data were used to fit a regression model. The SAS printout follows: _____________________________________________________________________ Analysis of Variance SOURCE DF SS MS F VALUE PROB > F MODEL 2 34593103.008 17296051.504 19.018 0.0001 ERROR 57 51840202.926 909477.24431 C TOTAL 59 86432305.933 ROOT MSE 953.66516 R-SQUARE 0.4002 DEP MEAN 3197.96667 ADJ R-SQ 0.3792 C.V. 29.82099 Parameter Estimates VARIABLE DF PARAMETER ESTIMATE STANDARD ERROR T FOR 0: PARAMETER = 0 PROB > |T| INTERCEPT 1 -373.526392 1258.1243396 -0.297 0.7676 SPEED 1 104.838940 22.36298195 4.688 0.0001 CHIP 1 3.571850 3.89422935 0.917 0.3629 OBS SPEED CHIP Dep Var PRICE Predict Value Std Err Predict Lower 95% Predict Upper 95% Predict Residual 1 33 286 5099.0 4464.9 260.768 3942.7 4987.1 634.1 Interpret the value of R 2 for the model. A) 40% of the time the model will capture the true value of PRICE. B) The model explains about 40% of the sample variation in PRICE. C) The correlation between PRICE, SPEED, and CHIP is .40. D) The probability of the model being a good predictor is only .40. 134561) As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): x 1 = average high school grade in mathematics (HSM) x 2 = average high school grade in science (HSS) x 3 = average high school grade in English (HSE) x 4 = SAT mathematics score (SATM) x 5 = SAT verbal score (SATV) The first-order model below was fit to data with the following results: E(y) = ß 0 + ß 1 x 1 + ß 2 x 2 + ß 3 x 3 + ß 4 x 4 + ß 5 x 5 _____________________________________________________________________ SOURCE DF SS MS F VALUE PROB > F MODEL 5 28.64 5.73 11.69 .0001 ERROR 218 106.82 0.49 TOTAL 223 135.46 ROOT MSE 0.700 R-SQUARE 0.211 DEP MEAN 4.635 ADJ R-SQ 0.193 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T FOR 0: PARAMETER = 0 PROB > |T| INTERCEPT 2.327 0.039 5.817 0.0001 X1 (HSM) 0.146 0.037 3.718 0.0003 X2 (HSS) 0.036 0.038 0.950 0.3432 X3 (HSE) 0.055 0.040 1.397 0.1637 X4 (SATM) 0.00094 0.00068 1.376 0.1702 X5 (SATV) -0.00041 0.0059 -0.689 0.4915 Test to determine if the model is adequate for predicting student GPA. Use ? = .01. 135562) What factors affect the sale price of oceanside condominium units? To answer this question, the following data were recorded for each of the n = 105 units sold at auction: y = Sale price ($thousands) x 1 = Floor height (1, 2, 3, ... , 8) x 2 = 1 if ocean view, 0 if bay view The first-order model below was fit to the data with the following results: E(y) = ß 0 + ß 1 x 1 + ß 2 x 2 _____________________________________________________________________ SOURCE DF SS MS F VALUE PROB > F MODEL 2 19.08 8.04 4.14 .0250 ERROR 102 197.96 1.94 TOTAL 104 217.04 ROOT MSE 1.393 R-SQUARE .088 VARIABLES PARAMETER ESTIMATE STANDARD ERROR T FOR 0: PARAMETER = 0 PROB > |T| INTERCEPT 17.770 .416 42.71 .0001 X 1 -.073 .053 -1.39 .1674 X 2 3.137 .222 14.08 .0001 Interpret the p-value for the variable X 1 . Assume you are testing the null hypothesis H 0 : ß 1 = 0 at ? = .10. A) Do not reject H 0 in favor of H a : ß 1 ? 0. B) Reject H 0 in favor of H a : B 1 > 0. C) Reject H 0 in favor of H a : ß 1 ? 0. D) Reject H 0 in favor of H a : ß 1 < 0. 136563) What factors affect the sale price of oceanside condominium units? To answer this question, the following data were recorded for each of the n = 105 units sold at auction: y = Sale price ($thousands) x 1 = Floor height (1, 2, 3, ... , 8) x 2 = 1 if ocean view, 0 if bay view The first-order model below was fit to the data with the following results: E(y) = ß 0 + ß 1 x 1 + ß 2 x 2 _____________________________________________________________________ SOURCE DF SS MS F VALUE PROB > F MODEL 2 19.08 8.04 4.14 .0250 ERROR 102 197.96 1.94 TOTAL 104 217.04 ROOT MSE 1.393 R-SQUARE .088 VARIABLES PARAMETER ESTIMATE STANDARD ERROR T FOR 0: PARAMETER = 0 PROB > |T| INTERCEPT 17.770 .416 42.71 .0001 X 1 -.073 .053 -1.39 .1674 X 2 3.137 .222 14.08 .0001 What are your recommendations concerning the term for floor height (x 1 )? Test at ? = .05. A) Drop floor height from the model since it is not a useful predictor of sale price. B) Keep floor height in the model since its ß-coefficient is not equal to 0. C) Keep floor height in the model since it is a useful linear predictor of sale price. D) It is too early to drop floor height from the model at this stage since it may become significant when higher order terms (e.g., interactions) are added to the model. 564) In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x 2 ) and the number of checks cashed per day (x 1 ). Data collected for n = 20 working days were used to fit the model: E(y) = ß 0 + ß 1 x 1 + ß 2 x 2 The SAS printout for the analysis follows: _____________________________________________________________________ Analysis of Variance SOURCE DF SS MS F VALUE PROB > F MODEL 2 7089.06512 3544.53256 13.267 0.0003 ERROR 17 4541.72142 267.16008 C TOTAL 19 11630.78654 137ROOT MSE 16.34503 R-SQUARE 0.6095 DEP MEAN 93.92682 ADJ R-SQ 0.5636 C.V. 17.40188 Parameter Estimates VARIABLE DF PARAMETER ESTIMATE STANDARD ERROR T FOR 0: PARAMETER = 0 PROB > |T| INTERCEPT 1 114.420972 18.6848744 6.124 0.0001 X1 1 -0.007102 0.00171375 -4.144 0.0007 X2 1 0.037290 0.02043937 1.824 0.0857 OBS X1 X2 Actual Value Predict Value Residual Lower 95% CL Predict Upper 95% CL Predict 1 7781 644 74.707 83.175 -8.468 47.224 119.126 Calculate a 95% confidence interval for ß 1 . A)-.007 ± .0007 B)-4.144 ± .0007 C)-.007 ± .0036 D)-.007 ± .0017 565) In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x 2 ) and the number of checks cashed per day (x 1 ). Data collected for n = 20 working days were used to fit the model: E(y) = ß 0 + ß 1 x 1 + ß 2 x 2 Suppose a 95% confidence interval for ß 1 is (-.02, -.01). Interpret this result. A) We expect to predict most (approximately 95%) of the daily number of man-hours worked to within a range of .01 to .02 of its true value. B) We are 95% confident that the daily number of man-hours worked decreases by an amount between .01 and .02 man-hour for each extra piece of mail sorted, holding number of checks cashed constant. C) We are 95% confident that the mean number of man-hours worked per day falls between .01 and .02. D) We are 95% confident that the daily number of man-hours worked decreases by an amount between .01 and .02 man-hour for each extra check cashed, holding number of pieces of mail sorted constant. 138566) During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first three tests. To test this claim, multiple regression will be used to model Test4 score (y), as a function of Test1 score ( x 1 ), Test 2 score (x 2 ), and Test3 score (x 3 ). [Note: All test scores range from 200 to 800, with higher scores indicative of a higher quality product.] Consider the model: E(y) = ß 1 + ß 1 x 1 + ß 2 x 2 + ß 3 x 3 The first-order model was fit to data for each of 12 units sampled from the production line. The results are summarized in the SAS printout. _____________________________________________________________________ SOURCE DF SS MS F VALUE PROB > F MODEL 3 151417 50472 18.16 .0075 ERROR 8 22231 2779 TOTAL 12 173648 ROOT MSE 52.72 R-SQUARE 0.872 DEP MEAN 645.8 ADJ R-SQ 0.824 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T FOR 0: PARAMETER = 0 PROB > |T| INTERCEPT 11.98 80.50 0.15 0.885 X1(TEST1) 0.2745 0.1111 2.47 0.039 X2(TEST2) 0.3762 0.0986 3.82 0.005 X3(TEST3) 0.3265 0.0808 4.04 0.004 Compute a 95% confidence interval for ß 3 . A) .33 ± 105 B) .33 ± .19 C) .33 ± .08 D) .33 ± 4.04 139567) During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first three tests. To test this claim, multiple regression will be used to model Test4 score (y), as a function of Test1 score ( x 1 ), Test 2 score (x 2 ), and Test3 score (x 3 ). [Note: All test scores range from 200 to 800, with higher scores indicative of a higher quality product.] Consider the model: E(y) = ß 1 + ß 1 x 1 + ß 2 x 2 + ß 3 x 3 The first-order model was fit to data for each of 12 units sampled from the production line. The results are summarized in the SAS printout. _____________________________________________________________________ SOURCE DF SS MS F VALUE PROB > F MODEL 3 151417 50472 18.16 .0075 ERROR 8 22231 2779 TOTAL 12 173648 ROOT MSE 52.72 R-SQUARE 0.872 DEP MEAN 645.8 ADJ R-SQ 0.824 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T FOR 0: PARAMETER = 0 PROB > |T| INTERCEPT 11.98 80.50 0.15 0.885 X1(TEST1) 0.2745 0.1111 2.47 0.039 X2(TEST2) 0.3762 0.0986 3.82 0.005 X3(TEST3) 0.3265 0.0808 4.04 0.004 Suppose the 95% confidence interval for ß 3 is (.15, .45). Which of the following statements is incorrect? A) We are 95% confident that the estimated slope for the Test4-Test3 line falls between .15 and .45 holding Test1 and Test2 fixed. B) At ? = .05, there is insufficient evidence to reject H 0 : ß 3 = 0 in favor of H a : ß 3 ? 0. C) We are 95% confident that the Test3 is a useful linear predictor of Test4 score, holding Test1 and Test2 fixed. D) We are 95% confident that the increase in Test4 score for every 1-point increase in Test3 score falls between .15 and .45 point, holding Test1 and Test2 fixed. 140568) In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x 1 ) and the number of checks cashed per day (x 2 ). Data collected for n = 20 working days were used to fit the model: E(y) = ß 0 + ß 1 x 1 + ß 2 x 2 The SAS printout for the analysis follows: _____________________________________________________________________ Analysis of Variance SOURCE DF SS MS F VALUE PROB > F MODEL 2 7089.06512 3544.53256 13.267 0.0003 ERROR 17 4541.72142 267.16008 C TOTAL 19 11630.78654 ROOT MSE 16.34503 R-SQUARE 0.6095 DEP MEAN 93.92682 ADJ R-SQ 0.5636 C.V. 17.40188 Parameter Estimates VARIABLE DF PARAMETER ESTIMATE STANDARD ERROR T FOR 0: PARAMETER = 0 PROB > |T| INTERCEPT 1 114.420972 18.68485744 6.124 0.0001 X1 1 -0.007102 0.00171375 -4.144 0.0007 X2 1 0.037290 0.02043937 1.824 0.0857 OBS X1 X2 Actual Value Predict Value Residual Lower 95% CL Predict Upper 95% CL Predict 1 7781 644 74.707 83.175 -8.468 47.224 119.126 Test to determine if there is a positive linear relationship between the number of man-hours worked, y, and the number of checks cashed per day, x 2 . Use ? = .05. 141Answer Key Testname: STATISTICS PRACTICE PROBLEMS 1) Statistics is the science of data that involves collecting, classifying, summarizing, organizing, analyzing, and interpreting numerical information. 2) C 3) A 4) Descriptive: 20% of the students sampled (or 1000) read at leat one best-seller each month. Inferential: Based on the survey, we estimate that about 20% of all high school students read at leat one best-seller each month. 5) The population of interest are all students at the university who park. The sample is the parking times of the 150 students that were collected by the university administrator. The variable of interest to the administrators is the parking time variable. 6) B 7) B 8) B 9) When a subset of the experimental units in the population is excluded so that these units have no possibility of being selected in the sample. 10) C 11) C 12) C 13) B 14) The stem will consist of the tens digit and range from 1 to 9. The leaves will be drawn in the appropriate stems based on the data values. Stem Leaves 1 0 2 3 4 5 2 7 6 6 9 7 6 7 9 8 7 8 5 9 3 8 2 9 7 2 4 9 0 15) A 16) C 17) D 18) A 19) D 20) C 21) D 22) D 23) A 24) A 25) D 26) C 27) C 28) B 29) C 142Answer Key Testname: STATISTICS PRACTICE PROBLEMS 30) µ is the mean price of the regular unleaded gasoline prices of all retail gas stations in the United States. ? is the standard deviation of the regular unleaded gasoline prices of all retail gas stations in the United States. x is the mean price of the regular unleaded gasoline prices collected from the 200 stations sampled. s is the standard deviation of the regular unleaded gasoline prices collected from the 200 stations sampled. 31) A 32) C 33) D 34) C 35) B 36) A 37) D 38) B 39) D 40) C 41) Changing the scale on the vertical axis, horizontal axis, or both can alter the impression conveyed by the graph. 42) 1) Check the axes and the size of units on each axis. 2) Ignore visual changes and concentrate on the actual numerical changes indicated in the graph. 43) C 44) 0.71 45) 26/400 46) B 47) A 48) D 49) B 50) A 51) D 52) A 53) B 54) B 55) B 56) Venn diagram: Let A = use golf regularly B = use tennis regularly 57) D 58) C 59) C 60) FALSE 143Answer Key Testname: STATISTICS PRACTICE PROBLEMS 61) P(uses golf or tennis regularly) = P(golf) + P(tennis) - P(both tennis and golf) = .61 + .50 - 0.18 = .93 62) A 63) B 64) FALSE 65) B 66) D 67) A 68) A 69) B 70) TRUE 71) B 72) A 73) C 74) B 75) D 76) C 77) D 78) B 79) D 80) µ = 1.596; ? = 1.098 81) FALSE 82) A 83) D 84) B 85) B 86) C 87) Let x = the number of the 14 cars with defective gas tanks. Then X is a binomial random variable with n = 14 and p = .30. P(more than half) = P(x > 7) = P(x ? 8) = 1 - P(x ? 7) = 1 - 0.968 = 0.032 (from a binomial probability table) 88) Let x = the number of the 12 hypertensive patients whose blood pressure drops. Then X is a binomial random variable with n = 12 and p = .5. P(x ? 10) = P(x = 10) + P(x = 11) + P(x = 12) = 0.019287 89) B 90) D 91) B 92) D 93) A 94) D 95) B 96) B 97) C 98) A 99) D 100) C 144Answer Key Testname: STATISTICS PRACTICE PROBLEMS 101) Let x = the number of death claims received per day. Then x is a Poisson random variable with ? = 3. P(x ? 7) = 1 - P(x ? 6) = 0.033509 102) Let x = the number of accidents that occur on the stretch of road during a month. Then x is a Poisson random variable with ? = 7.8. P(x < 2) = P(x = 0) + P(x = 1) = 0.003606 103) Let x = the number of babies born during a one hour period at this hospital's maternity wing. Then x is a Poisson random variable with ? = 6. P(x = 5) = 0.160623 104) D 105) B 106) A 107) D 108) C 109) C 110) A 111) C 112) The population consists of N = 11 transplants. Define a "success" as a failed liver transplant. The number of "successes" is r = 4, and the sample size is n = 4. Then x is the number of failed liver transplants the sample of n = 4. We use the hypergeometric distribution: p(x) = r x N - r n - x N n = 4 x 11 - 4 4 - x 11 4 = 4 x 7 4 - x 11 4 P(none of the 4) = P(x = 0) = p(0) = 4 0 7 4 11 4 = 4! 0!4! 7! 4!3! 11! 4!7! = 0.106061 145Answer Key Testname: STATISTICS PRACTICE PROBLEMS 113) The population consists of N = 14 phones. Define a "success" to be a faulty phone. The number of "successes" is r = 5, and the sample size is n = 2. Then x is the number of faulty phones in the sample of n = 2. We use the hypergeometric distribution: p(x) = r x N - r n - x N n = 5 x 14 - 5 2 - x 14 2 = 5 x 9 2 - x 14 2 P(both faulty phones) = P(x = 2) = p(2) = 5 2 9 0 14 2 = 5! 2!3! · 9! 0!9! 14! 2!12! = 5 · 4 · 1 14 · 13 = 0.10989 114) C 115) D 116) FALSE 117) TRUE 118) A 119) B 120) D 121) B 122) C 123) D 124) A 125) A 126) B 127) A 128) B 129) A 130) B 131) C 132) Let x = high temperature in August. Then x is a uniform random variable with c = 145°F and d = 165°F. P(x > a) = d - a d - c P(x > 150) = 165 - 150 165 - 145 = 15 20 = .75 146Answer Key Testname: STATISTICS PRACTICE PROBLEMS 133) Let x = ball bearing diameter. Then x is a uniform random variable with c = 3.5 and d = 9.5. P(x < a) = a - c d - c P(x < 5.5) = 5.5 - 3.5 9.5 - 3.5 = 2 6 = 0.33 134) µ = c + d 2 = 10 + 80 2 = 45 135) Let x = gallons pumped per minute. Then x is a uniform random variable with c = 6.5 and d = 7.5. P(x < a) = a - c d - c P(x < 6.75) = 6.75 - 6.5 7.5 - 6.5 = 0.25 1 = 0.25 136) A 137) D 138) C 139) D 140) B 141) A 142) D 143) C 144) C 145) Let x be the internal rate of return. Then x is a normal random variable with µ = 35% and ? = 3%. To determine the probability that x is at least 30.5%, we need to find the z-value for x = 30.5%. z = x - µ ? = 30.5 - 35 3 = -1.5 P(x ? 30.5%) = P(-1.5 ? z) = .5 + P(-1.5 ? z ? 0) = .5 + .4332 = .9332 146) A 147) C 148) C 149) D 150) A 151) B 152) D 153) B 154) C 155) D 156) A 157) A 158) B 147Answer Key Testname: STATISTICS PRACTICE PROBLEMS 159) Let x be the internal rate of return. Then x is a normal random variable with µ = 23% and ? = 3%. To determine the probability that x exceeds 29%, we need to find the z-value for x = 29%. z = x - µ ? = 29 - 23 3 = 2 P(x > 29%) = P(z ? 2) = .5 - P(0 ? z ? 2) = .5 - .4772 = .0228 160) Let x be a score on this exam. Then x is a normally distributed random variable with µ = 490 and ? = 72. We want to find the value of x 0 , such that P(x > x 0 ) = .10. The z-score for the value x = x 0 is z = x 0 - µ ? = x 0 - 490 72 . P(x > x 0 ) = P z > x 0 - 490 72 = .10 We find x 0 - 490 72 ? 1.28. x 0 - 490 = 1.28(72) ? x 0 = 490 + 1.28(72) = 582.16 161) Let x be a score on this exam. Then x is a normally distributed random variable with µ = 410 and ? = 72. We want to find the value of x 0 , such that P(x > x 0 ) = .80. The z-score for the value x = x 0 is z = x 0 - µ ? = x 0 - 410 72 . P(x > x 0 ) = P z > x 2 - 410 72 = .80 We find x 0 - 410 72 ? -.84. x 0 - 410 = -.84(72) ? x 0 = 410 - .84(72) = 349.52 162) Let x be the tread life of this brand of tire. Then x is a normal random variable with µ = 60,000 and ? = 55. To determine what proportion of tires fail before reaching 53,400 miles, we need to find the z-value for x = 53,400. z = x - µ ? = 53,400 - 60,000 55 = -1.20 P(x ? 53,400) = P(z ? -1.20) = .5 - P(-1.20 ? z ? 0) = .5 - .3849 = .1151 148Answer Key Testname: STATISTICS PRACTICE PROBLEMS 163) Let x be the number of tomatoes sold per day. Then x is a normal random variable with µ = 538 and ? = 30. To determine if all 83 tomatoes will be sold, we need to find the z-value for x = 496. z = x - µ ? = 496 - 538 30 = -1.4 P(x ? 496) = P(z ? -1.4) = .5 + P(-1.4 ? z ? 0) = .5 + .4192 = .9192 164) Let x be the number of tomatoes sold per day. Then x is a normal random variable with µ = 135 and ? = 30. We want to find the value x 0 , such that P(x > x 0 ) = .015. The z-value for the point x = x 0 is z = x - µ ? = x 0 - 135 30 . P(x > x 0 ) = P(z > x 0 - 135 30 )= .015 We find x 0 - 135 30 = 2.17 x 0 - 135 = 2.17(30) ? x 0 = 135 + 2.17(30) = 200 165) It is not reasonable to assume that the heights are normally distributed since the histogram has an approximately uniform distribution. 166) C 167) D 168) A 169) B 170) C 171) TRUE 172) D 173) C 149Answer Key Testname: STATISTICS PRACTICE PROBLEMS 174) D 175) D 176) A 177) C 178) B 179) B 180) B 181) D 182) x is a binomial random variable with n = 96 and p = 0.41. z = (x + .5) - np np(1 - p) = (46 + .5) - 96(0.41) 96(0.41)(1 - 0.41) = 1.48 183) Let x be the number of the 69 applications rejected. Then x is a binomial random variable with n = 69 and p = 0.18. z = (x - .5) - np np(1 - p) = (64 - .5) - 69(0.18) (69)(0.18)(1 - 0.18) = 16.01 184) cannot use normal distribution 185) can use normal distribution 186) FALSE 187) TRUE 188) B 189) A 190) C 191) A 192) D 193) B 194) C 195) C 196) A 197) A 198) A 199) C 200) B 201) B 202) A 203) A 204) Let x = life length. Then x is an exponential random variable with ? = 5400 hours. P(x > a) = e -a/? P(x > 3240) = e -3240/5400 = e -.6 = .548812 205) Let x = shelf life. Then x is an exponential random variable with ? = 3. P(x ? a) = e -a/? P(x ? 6) = e -6/3 = e -2 = .135335 206) Let x = shelf life. Then x is an exponential random variable with ? = 5. P(x < a) = 1 - e -a/? P(x < 15) = 1 - e -15/5 = 1 - e -3 = 1 - .049787 = .950213 150Answer Key Testname: STATISTICS PRACTICE PROBLEMS 207) Let x = life length. Then x is an exponential random variable with ? = 2400. P(x < a) = 1 - e -a/? P(x < 3000) = 1 - e -3000/2400 = 1 - e -1.25 = 1 - .286505 = .713495 208) C 209) D 210) C 211) A 212) 1 3.5 6 8.5 11 13.5 16 213) E(x) = (5)( 1 4 ) + (10)( 1 4 ) + (15)( 1 4 ) + (20)( 1 4 ) = 12.5 E(x) = (5)( 1 16 ) + ( 15 2 )( 2 16 ) + (10)( 3 16 ) + ( 12.5 2 )( 4 16 ) + (15)( 3 16 ) + ( 35 2 )( 2 16 ) + (20)( 1 16 ) = 12.5 214) B 215) D 216) D 217) FALSE 218) FALSE 219) FALSE 220) A 221) A 151Answer Key Testname: STATISTICS PRACTICE PROBLEMS 222) P(x > 10.45) = p z > 10.45 - 10.50 .2/ 100 = P (z > -2.5) = .5 + .4938 = .9938 223) D 224) C 225) B 226) B 227) B 228) A 229) By the Central Limit Theorem, the sampling distribution of x is approximately normal with µ x = µ = 10 minutes and ? x = ? n = 2.1 40 = 0.3320 minutes. 230) C 231) The standard error is ? x = ? n . If the standard error is desired to be 10, we get: 10 = ?/ n = 100 n ? n · 10 = 100 ? n = 100 10 = 10 ? n = 100 232) C 233) P(S 2 > 0.5) = P (n - 1)S 2 ? 2 > (29)(0.5) 0.3 = P(X 2 > 48.33) < 0.01 234) P(S 2 < k) = 0.10 ? P (n - 1)S 2 ? 2 > 29k 0.3 = 0.10 ? P(X 2 < 96.67k) = 0.10 ? 96.67k = 19.768 ? = 0.2045 152Answer Key Testname: STATISTICS PRACTICE PROBLEMS 235) P(s>0.7?)=P s 2 ? 2 >0.49 =P (n-1)s 2 ? 2 >(24)(.49) =P(x 2 >11.76)>0.975 236) P(S 2 < k? 2 ) = 0.90 ? P s 2 ? 2 = 90 ? P (n - 1)S 2 ? 2 > 24k = 0.90 ?P(x 2 <24k)?24k=33.196?k=1.383 or 13.83% 237) We need to obtain values K L and K U such that P s 2 ? 2 < K 2 L = 0.025 and P s 2 ? 2 < K 2 u = 0.025 Now, 0.025 = P (n - 1)S 2 ? 2 > 14K 2 L ? 14K 2 L = 5.629 ? K 2 L = 0.402 ? K L = 0.634, and .025 = (n - 1)S 2 ? 2 > 14K 2 U ? 14K 2 U = 26.119 ? K 2 U = 1.866 ? K U = 1.366 238) A 239) D 240) B 241) D 242) B 243) C 244) B 245) B 246) D 247) C 248) C 249) D 250) A 251) A 252) B 253) A 254) B 255) A 256) To determine the sample size necessary to estimate p, we use n = z ?/2 B 2 pq For confidence coefficient .99, 1 - ? = .99 ? ? = 1 - .99 = .01. ?/2 = .01/2 = .005. z ?/2 = z .005 = 2.575. Since no estimate of p exists, we use p = q = .5. n = 2.575 .03 2 (.5)(.5) = 1841.84028. Round up to n = 1842. 257) To determine the sample size necessary to estimate p, we use n = z ?/2 B 2 p(1 - p). For confidence coefficient .98, 1 - ? = .98 ? ? = 1 - .98 = .02. ?/2 = .02/2 = .01. z ?/2 = z .01 = 2.33. n = 2.33 .01 2 (.75)(1 - .75) = 10,179.1875. Round up to n = 10,180. 153Answer Key Testname: STATISTICS PRACTICE PROBLEMS 258) To determine the sample size necessary to estimate µ, we use n = z ?/2 B 2 ? 2 . For confidence coefficient .95, 1 - ? = .95 ? ? = 1 - .95 = .05. ?/2 = .05/2 = .025. z ?/2 = z .025 = 1.96. n = 1.96 48 2 280 2 = 130.7211. Round up to n = 131. 259) To determine the sample size necessary to estimate µ, we use n = z ?/2 B 2 ? 2 . For confidence coefficient .99, 1 - ? = .99 ? ? = 1 - .99 = .01. ?/2 = .01/2 = .005. z ?/2 = z .005 = 2.575. n = 2.575 300 2 1675 2 = 206.7005. Round up to n = 207. 260) To determine the sample size necessary to estimate µ, we use n = z ?/2 B 2 ? 2 . For confidence coefficient .98, 1 - ? = .98 ? ? = 1 - .98 = .02. ?/2 = .02/2 = .01. z ?/2 = z .01 = 2.33. n = 2.33 .1 2 2.4 2 = 3127.0464. Round up to n = 3128. 261) B 262) FALSE 263) TRUE 264) C 265) A 266) C 267) C 268) D 269) A 270) B 271) D 272) B 273) Let p = the true fraction of crimes in the area in which some type of firearm was reportedly used. p = 380 600 = .6333 and q ^ = 1 - p ^ = 1 - .6333 = .3667. The confidence interval for p is p ^ ± z ?/2 p ^ q ^ n . For confidence coefficient .95, 1 - ? = .95 ? ? = 1 - .95 = .05. ?/2 = .05/2 = .025. z ?/2 = z .025 = 1.96. The 95% confidence interval is: .6333 ± 1.96 .6333(.3667) 600 = .6333 ± .0386 154Answer Key Testname: STATISTICS PRACTICE PROBLEMS 274) For confidence coefficient .90, 1 - ? = .90 ? ? = 1 - .90 = .1. ?/2 = .1/2 = .05. z ?/2 = z .05 = 1.645. The 90% confidence interval for p is: p ^ ± z ?/2 p ^ q ^ n ? .30 ± 1.645 .30(.70) 505 ? .30 ± .0335 275) B 276) A 277) D 278) B 279) D 280) A 281) C 282) A 283) A 284) B 285) B 286) D 287) C 288) D 289) B 290) C 291) A 292) D 293) B 294) B 295) C 296) A 297) D 298) C 299) For confidence coefficient .95, 1 - ? ? ? = 1 - .95 = .05. ?/2 = 0.05/2 = 0.025. With df = n - 1 = 17 - 1 = 16, t 0.025 = 2.120. The 95% confidence interval is: x ± t ?/2 s n = 13,800 ± 2.120 800 17 = (13,388.66, 14,211.34) For this interval to be valid, we must assume that the population of resale values for all 5 year old foreign sedans of this model follows an approximately normal distribution. 300) We are 97% confident that the average total compensation of CEOs in the service industry is contained in the interval $2,181,260 to $5,836,180. 301) No, the average total compensation is not $1,500,000 and we are 97% sure of this statement. This is because the value $1,500,000 is not contained in the 97% confidence interval for µ. 302) Your friend could be correct. $45,000 is contained in the 90% confidence interval. It cannot be ruled out as a possible value for the mean sales price. 155Answer Key Testname: STATISTICS PRACTICE PROBLEMS 303) For confidence coefficient .95, 1 - ? = .95 ? ? = 1 - .95 = .05. ?/2 = .05/2 = .025. With n - 1 = 23 - 1 = 22 degrees of freedom, t ?/2 = t .025 = 2.074. The 95% confidence interval is: x ± t .025 s n = 131 ± 2.074 26 23 ? 131 ± 11.244 304) B 305) B 306) D 307) D 308) C 309) C 310) For confidence coefficient .99, 1 - ? ? ? = 1 - .99 = .01. ? ?/2 = .01/2 = .005 ? z .005 = 2.575. The confidence interval is: x ± z ?/2 s n = 12.00 ± 2.575 2.90 48 = 12.00 ± 1.078 = ($10.92, $13.08) We are 99% confident that the average spent on food at a single professional football game is between $10.92 and $13.08. 311) For confidence coefficient .95, 1 - ? = .95 ? ? = 1 - .95 = .05. ?/2 = .05/2 = .025. ? z ?/2 = z .025 = 1.96. The 95% confidence interval is: x ± z ?/2 s n = 24.8 ± 1.96 2.6 86 ? 24.8 ± .550 = (24.250, 25.350) 312) A 313) An increase in the sample size reduces the sampling variation of the point estimate as it is calculated as ?/ n. The larger the sample size, the smaller this variation which leads to narrower intervals. 314) TRUE 315) TRUE 316) Use the finite population correction factor when: n/N > .05. 317) The finite population correction factor is used when the sample size is large relative to the size of the population. 318) A 319) D 320) D 321) A 322) B 323) A 324) A 325) B 326) A 327) D 328) B 329) D 330) C 331) FALSE 332) To determine if the new method is more accurate in detecting cancer than the old method, we test: H 0 : p = .21 vs. H a : p < .21 156Answer Key Testname: STATISTICS PRACTICE PROBLEMS 333) To determine if the mean yield for the soybeans differs from 529 bushels per acre, we test: H 0 : µ = 529 vs. H a : µ ? 529 334) C 335) C 336) B 337) C 338) C 339) TRUE 340) FALSE 341) FALSE 342) A 343) D 344) B 345) B 346) C 347) A 348) D 349) A 350) C 351) C 352) To determine the mean time has been reduced, we test: H 0 : µ = 70 vs. H a : µ < 70 The rejection region requires ? = .10 in the lower tail of the z distribution. From a z table, we find z .10 = 1.28. The rejection region is z < -1.28. 353) To determine if the mean exceeds 840 hours, we test: H 0 : µ = 840 vs. H a : µ > 840 The rejection region requires ? = .01 in the upper tail of the z distribution. From a z table, we find z .01 = 2.33. The rejection region is z > 2.33. 354) To determine if the mean life exceeds 1000 hours, we test: H 0 : µ = 1000 vs. H a : µ > 1000 The test statistic is z = x - µ 0 ?/ n ? x - µ 0 s/ n = 1020 - 1000 70/ 49 = 2. The observed significance level for the test is p = P(z > 2) = .5 - P(0 < z < 2) = .5 - .4772 = .0228. Using ? = .05, ? > p-value = .0228, so H 0 can be rejected. There is sufficient evidence to indicate the average life of the new bulbs exceeds 1000 hours when testing at ? = .05. 355) Since ? = .01 > p-value = .0013, H 0 can be rejected. There is sufficient evidence to indicate that the average tuition and fees for four-year private colleges exceeds $8934 for the 1999-2000 academic year. 356) B 357) A 157Answer Key Testname: STATISTICS PRACTICE PROBLEMS 358) A 359) D 360) C 361) D 362) A 363) D 364) Since ? = .01 > p-value = .0008, H 0 can be rejected. There is sufficient evidence to indicate that the average tuition and fees for four-year private colleges exceeds $8446 for the 1999-2000 academic year. 365) D 366) TRUE 367) A 368) C 369) A 370) C 371) A 372) A 373) A 374) A 375) D 376) A 377) A 378) B 379) C 380) D 381) D 382) A 383) B 384) To determine the average price of VCR's in 1998 exceeds $209, we test: H 0 : µ = 209 vs. H a : µ > 209. The test statistic is t = x - µ 0 s/ n = 279 - 209 70/ 16 = 4.0 The rejection region requires ? = .05 in the upper tail of the t-distribution with df = n - 1 = 16 - 1 = 15. The rejection region is t > t .05 = 1.753. Rejection H 0 if t > 1.753. Since the observed value of the test statistic falls in the rejection region, H 0 is rejected. There is sufficient evidence to indicate that the average VCR price in 1998 exceeds $209 when testing at ? = .05. 385) The rejection region requires ?/2 = .05/2 = .025 in both tails of the t distribution with df = n - 1 = 25 - 1 = 24. The rejection region is t > 2.064 or t < -2.064. 386) C 387) B 388) C 389) D 390) D 391) A 392) D 393) C 158Answer Key Testname: STATISTICS PRACTICE PROBLEMS 394) D 395) A 396) A 397) A 398) B 399) The test statistic is z = p ^ - p 0 p 0 q 0 n p ^ = 7 60 = .117 The test statistic is z = .117 - .15 .15(.85) 60 = -.72 400) To determine if the sample size is large enough for the test of hypothesis to work properly, we need to calculate the interval p 0 ± 3? p ^ . p 0 ± 3? p ^ = p 0 ± 3 p 0 q 0 n = .20 ± 3 .20(.80) 80 = .20 ± 3(.045) ? (.066, .334) Since this interval does not include the values of 0 or 1, the sample size of n = 80 is large enough for the test of hypothesis to work properly. 401) To determine if more than 85% of the firms do not offer any child-care benefits, we test: H 0 : p = .85 vs. H a : p > .85 The rejection region requires ? = .10 in the upper tail of the z distribution. The rejection region is z > z .10 = 1.28. 402) At ? = .05, ? < p-value = .1130, so H 0 cannot be rejected. There is insufficient evidence to indicate that more than 80% of the firms do not offer any child-care benefits. 403) A 404) Since the alternative hypothesis is H a : µ > 30, the test is one-tailed. Thus, ? = .025 is required in the upper tail of the z distribution, and we have z .025 = 1.96. The value of x on the border between the rejection region and the acceptance region is found using z = x - 30 ?/ n ? x = z ? n + 30 ? x = 1.96 7 49 + 30 ? x = 31.96 ß = P(x < 31.96, when µ a = 31) = P z < 31.96 - 31 7/ 49 = P(z < 0.96) = .5 + .3315 = .8315 The power is 1 - ß = 1 - .8315 = .1685. 405) B 406) C 407) C 159Answer Key Testname: STATISTICS PRACTICE PROBLEMS 408) Since the alternative hypothesis is H a : µ > 30, the test is one-tailed. Thus, ? = .025 is required in the upper tail of the z distribution, and we have z .025 = 1.96. The value of x on the border between the rejection region and the acceptance region is found using z = x - 30 ?/ n ? x = z ? n + 30 ? x = 1.96 7 49 + 30 ? x = 31.96 ß = P(x < 31.96, when µ a = 31) = P z < 31.96 - 31 7/ 49 = P(z < 0.96) = .5 + .3315 = .8315 The power is 1 - ß = 1 - .8315 = .1685. 409) Since the alternative hypothesis is H a : µ > 30, the test is one-tailed. Thus, ? = .025 is required in the upper tail of the z distribution, and we have z .025 = 1.96. The value of x on the border between the rejection region and the acceptance region is found using z = x - 30 ?/ n ? x = z ? n + 30 ? x = 1.96 7 49 + 30 ? x = 31.96 ß = P(x < 31.96, when µ a = 32) = P z < 31.96 - 32 7/ 49 = P(z < -.04) = .5 - .0160 = .4840 410) The test statistic is X 2 = (n - 1)s 2 ? 2 0 = (36 - 1).103 .07 = 51.500. 411) A 412) To determine if the test achieved the desired dispersion, we test: H 0 : ? 2 = 4900 vs. H a : ? 2 > 4900 413) We test H 0 : ? 2 = 4900 H a : ? 2 < 4900 The test statistic is X 2 = (n -1)s 2 ? 2 = (30 -1)1,943 4900 = 11.499 The rejection region requires ? = .025 in the upper tail of the X 2 distribution with n - 1 = 30 - 1 = 29 df. So X 2 .025 = 45.722. The rejection region is X 2 > 45.722. Since the observed value of the test statistic does not fall in the rejection region (X 2 = 11.499 ? 45.722), H 0 cannot be rejected. There is insufficient evidence to indicate the variance is greater than 4900 at ? = .025. 414) The test statistic is X 2 = (n - 1)s 2 ? 2 0 = (25 - 1).118 .05 = 56.640. 160Answer Key Testname: STATISTICS PRACTICE PROBLEMS 415) The rejection region requires ? = .10 in the upper tail of the X 2 distribution with n - 1 = 41 - 1 = 40 df. From Table VII, Appendix A, X 2 .10 = 51.805. The rejection region is X 2 > 51.805. 416) Since ? = .01 > p = .0031, H 0 can be rejected. There is sufficient evidence to indicate that the variance in the amount of serum injected exceeds .06. 417) A 418) A 419) A 420) B 421) A 422) A 423) C 424) D 425) D 426) B 427) A 428) C 429) B 430) A 431) D 432) C 433) D 434) The matched pairs confidence interval for µ d is xd ± t ?/2 s d n Confidence coefficient .90 ? ? = 1 - .90 = .10. ?/2 = .10/2 = .05. t .05 = 2.132 with n - 1 = 5 - 1 = 4 df. The 90% confidence interval is: 5 ± 2.132 1.58 5 ? 5 ± 1.51 ? (3.49, 6.51) 435) To determine if the diet is effective at reducing weight, we test: H 0 : µ D = 0 H a : µ D > 0 The test statistic is t = xd - 0 s d / n = 5 - 0 1.58 5 = 7.07 The rejection region requires ? = .10 in the upper tail of the t distribution with df = n - 1 = 5 - 1 = 4. t .10 = 1.533. The rejection region is t > 1.533. Since the observed value of the test statistic falls in the rejection region (t = 7.07 > 1.533), H 0 is rejected. There is sufficient evidence to indicate that the diet is effective at reducing weight when testing at ? = .10. 436) D 437) D 438) B 439) D 440) A 161Answer Key Testname: STATISTICS PRACTICE PROBLEMS 441) C 442) B 443) B 444) C 445) A 446) D 447) C 448) D 449) B 450) A 451) D 452) C 453) C 454) A 455) C 456) C 457) D 458) D 459) B 460) C 461) B 462) C 463) D 464) A 465) A 466) B 467) A 468) B 469) B 470) B 471) A 472) D 473) B 474) A 475) D 476) C 477) B 478) D 479) C 480) D 481) D 482) C 483) C 484) A 485) B 486) B 487) D 488) A 162Answer Key Testname: STATISTICS PRACTICE PROBLEMS 489) The data was collected using the completely randomized sampling design. The one factor in the study is compensation system which has three levels: commissioned, fixed salary, and commission plus salary. The response variable is amount of sales recorded for a month. 490) To determine if a difference exists in the mean sale amounts among the three compensation systems, we test: H 0 : µ 1 = µ 2 = µ 3 vs. H a : At least two means differ The test statistic is F = 3.17. The rejection region requires ? = .025 in the upper tail of the F distribution with v 1 = p - 1 = 3 - 1 = 2 df and v 2 = n - p = 15 - 3 = 12 df. So F .025 = 3.89, and the rejection region is F > 3.89. Since the observed value of the test statistic does not fall in the rejection region (F = 3.17 ? 3.89), H 0 cannot be rejected. There is insufficient evidence to indicate a difference in the mean sale amounts among the three compensation systems when testing at ? = .025. 491) To determine if the average home values differ for the two communities, we test: H 0 : µ 1 = µ 2 vs. H a : µ 1 ? µ 2 The test statistic is F = .21. The p-value for the test is p = .6501. Since ? = .05 < p-value = .6501, H 0 cannot be rejected. There is insufficient evidence to indicate that the average home values differ for the two communities. 492) C 493) a. S df SS MS F T 2 25.2 12.6 2.26 E 11 61.2 5.56 T 13 86.4 b. 3 c. No; F = 2.26 is less than F .05 = 3.98 with df = 2 and 11. 494) A 495) A 496) B 497) B 498) D 499) C 500) The data were collected using a randomized block design. The factors are supermarket (levels = A, B, and C) and item (levels: the 60 items selected). The 60 items represent the blocks that are used to compare the three supermarkets (treatments). The response variable is the cost of an item. 501) To determine if a difference exists in the mean prices of the three supermarkets, we test: H 0 : µ A = µ B = µ C vs. Ha: At least two means differ The test statistic is F = 39.23. The p-value of this test is p = 0.0001. Since ? = .01 > p = 0.0001, H 0 is rejected. There is sufficient evidence to indicate a difference in the mean prices of the three supermarkets. 502) D 163Answer Key Testname: STATISTICS PRACTICE PROBLEMS 503) SOURCE df SS MS F _________________________________________________ Treatments 2 86.22 43.11 13.15 Blocks 2 0.889 0.444 0.136 Error 4 13.11 _________________________________________________ Total 8 100.22 504) B 505) D 506) a. Blocking on participants controls possible participant-to-participant variation in rating the ice cream flavors. b. SOURCE df SS MS F ____________________________________________________ Flavors 2 357.56 178.78 3.83 Participants 2 105.56 3.8430 12.98 Error 4 55.111 _____________________________________________________ Total 8 518.23 c. Yes. Since F = 12.98 > F .05 = 6.94 (df1 = 2, df2 = 4), we reject the null hypothesis of equal means. There is sufficient statistical evidence that the three flavors of ice cream have different mean ratings. 507) TRUE 508) TRUE 509) A 510) D 511) B 512) B 513) D 514) A 515) D 516) C 517) D 518) A 519) The main effect factors, agency and medium, would not be tested since the interaction of these factors is a significant factor. 520) The data were collected using a 2 x 2 factorial design with 10 replications. The two factors in the experiment are subject visibility (levels: visible and not visible) and test taker success (levels: top 20% and bottom 20%). The treatments are the 2 x 2 = 4 combinations of the factor levels: Visible, Top 20% Visible, Bottom 20% Not Visible, Top 20% Not Visible, Bottom 20% The response variable is the latency to feedback times. 164Answer Key Testname: STATISTICS PRACTICE PROBLEMS 521) To determine if subject visibility and test taker success interact, we test: H 0 : Subject visibility and test taker success do not interact. H a : Subject visibility and test taker success do interact. The test statistic is F = 10.45. The p-value for this test is p = .002. Since ? = .01 > p = .002, H 0 is rejected. There is sufficient evidence to indicate that subject visibility and test taker success interact. 522) Source df SS MS F _____________________________________________________________________ A 3 649.8 216.60 0.68 B 1 284.50 284.50 0.89 AB 3 1583.70 527.90 1.65 ERROR 16 5124.80 320.30 _____________________________________________________________________ Total 23 7642.80 523) a. FACTOR B Level 1 2 3 FACTOR A 1 4.1 5.1 6.2 2 5.7 5.2 8.9 b. Since F = 1.48678 < F .05 = 5.14 (df1 = 2, df2 = 6), we do not reject the null hypothesis of no interaction. No, there is not significant evidence of interaction. c. Yes, since the null hypothesis of no interaction was not rejected, we should test the main effects. For factor A, F = 0.11851 < F .05 = 5.99 (df1 = 1, df2 = 6). We do not reject the null hypothesis of equal means. For factor B, F = 0.55391 < F .05 = 5.14 (df1 = 2, df2 = 6). We do not reject the null hypothesis of equal means. 524) A 525) TRUE 526) C 527) C 528) Assumption 1: The mean of the probability distibution of ? is 0. Assumption 2: The variance of the probability distibution of ? is constant for all settings of the incependent variable, x. Assumption 3: The probability distibution of ? is normal. Assumption 4: The values of ? associated with any two observed values of y are independent. 529) B 530) ß ^ 1 = -.08365. For every 1 mile per hour increase in the maximum attained speed of a new car, we estimate the elapsed 0 to 60 acceleration time to decrease by .08365 seconds. 165Answer Key Testname: STATISTICS PRACTICE PROBLEMS 531) ß ^ 1 = SS xy SS xx = 2,862.3375 1,006.3773 = 2.4804 ß ^ 0 = y - ß ^ 1x = 95.0625 - 2.4804(21.2675) = 42.3106 The least squares prediction equation is y ^ = 42.3106 + 2.4804x. 532) a. E(y) = ß 0 + ß 1 x b. y ^ = ß ^ 0 + ß ^ 1x = 177.52 - .8195x c. We would expect approximately 168 grunts after feeding a warthog that was just born. However, since the value 0 in outside the range of the original data set, this estimate is highly unreliable. d. For each additional day, we estimate the number of grunts will decrease by .8195. 533) C 534) A 535) A 536) C 537) D 538) C 539) B 540) A 541) D 542) A 543) B 544) A 545) A 546) A 547) D 548) A 549) A 550) A 551) A 552) B 553) B 554) D 555) D 556) C 557) C 558) A 559) B 560) B 166Answer Key Testname: STATISTICS PRACTICE PROBLEMS 561) To determine if the model is useful for predicting y, we test: H 0 : ß 1 = ß 2 = ß 3 = ß 4 = ß 5 = 0 H a : At least one ß i ? 0 The test statistic is F = 11.69. The p-value is p = .0001. At ? = .01, ? > p so H 0 is rejected. There is sufficient evidence to indicate the model is adequate for predicting student GPA. 562) A 563) D 564) C 565) B 566) B 567) B 568) To determine if number of checks cashed per day is a positive linear predictor of number of man-hours worked, we test: H 0 : ß 2 = 0 H a : ß 2 > 0 The test statistic is t = 1.824 The p-value is p = .0857/2 = .04285 At ? = .05, ? > p and H 0 is rejected. There is sufficient evidence to indicate that the number of checks cashed per day is a positive linear predictor of the number of man-hours worked at ? = .05. 167