Final Exam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The average age of the students in a statistics class is 22 years. Does this statement describe descriptive or inferential statistics? A) Inferential statistics B) Descriptive statistics 1) 2) A study attempted to estimate the proportion of Florida residents who were willing to spend more tax dollars on protecting the Florida beaches from environmental disasters. Twenty-five hundred Florida residents were surveyed.Which of the following describes the variable of interest in the study? A) the response to the question, "Are you willing to spend more tax dollars on protecting the Florida beaches from environmental disasters?" B) the response to the question "Do you live along the beach?" C) the 2500 Florida residents surveyed D) the response to the question "Do you use the beach?" 2) 3) As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. Identify the experimental unit of interest for this study. A) the current price (or closing price) of a NYSE stock B) a single stock traded on the NYSE C) the 500 NYSE stocks that current prices were collected from D) the entire set of stocks that are traded on the NYSE 3) 4) An usher records the number of unoccupied seats in a movie theater during each viewing of a film. Identify the type of data collected. B) quantitative A) qualitative 4) 5) The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 330 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watches television. Identify how the data were collected in this study. A) from a published source B) observationally C) from a designed experiment D) from a survey 5) 6) Because of the possible legal consequences, many people in a sample of the U.S. population chose not to participate in a survey regarding illegal drug use. What type of problem has occurred? A) measurement error B) selection bias C) nonresponse bias 6) A-1 7) A sociologist recently conducted a survey of senior citizens who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows: 70 76 71 65 62 75 63 94 70 89 68 91 78 83 77 78 67 64 72 66 7) _ _ __ 88 92 83 75 84 Find the median of the observations. B) 76 A) 75 C)72 D) 75.5 8) 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 98 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. If nothing is known about the shape of the distribution, give an interval that will contain the speeds of at least eight-ninths of the player's serves. A) 38 mph to 158 mph B) 53 mph to 143 mph C) 143 mph to 188 mph D) 68 mph to 128 mph 8) 9) If nothing is known about the shape of a distribution, what percentage of the observations fall within 3 standard deviations of the mean? A) at least 89% B) approximately 99.7% C) approximately 0.3% D) at most 11 % 9) 10) Given a data set, which of the following is most likely to be the percentage of data within three standard deviations of the mean? A) 95% B) 70% C) 85% D) 65% 10) 11) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the standard deviation of the expenditures was calculated to be $100. Suppose a randomly selected student reported that their textbook expenditure was $700. Calculate the z-score for this student's textbook expenditure. A)-3 B)+3 C)+2 D)-2 11) 12) An experiment consists of rolling two dice and summing the resulting values. Which of the following is not a sample point for this experiment? A)2 B)7 C)6 D)l 12) _ __ 13) Two chips are drawn at random and without replacement from a bag containing four blue chips and three red chips. Find the probability of drawing two red chips. 13) _ __ A) 9 49 B) 1 C) 1 u 7 D) ~ 7 Compute. 14) (~) A)6 14) - - C) 2 B) 35 A-2 D) 840 Solve the problem. 15) Suppose that for a certain experiment P(A) = .47 and P(B) = .25 and P(A n B) = .14. Find P(A u B). A) .58 B) .72 C) .36 D) .86 16) Use the standard normal distribution to find P(-2.25 < z < 1.25). A) .8944 B) .4878 C) .8821 D) .0122 17) Use the standard normal distribution to find P(z < -2.33 or z > 2.33). A) .0606 B) .0198 C) .7888 15) _ __ D) .9809 16) - - - 17) 18) 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 2400 miles. What is the probability a certain tire of this brand will last between 54,960 miles and 55,680 miles? A) .9813 B) .4649 C) .4920 D) .0180 18) 19) Suppose a random variable xis best described by a normal distribution with= 60 and a= 7. Find the z-score that corresponds to the value x = 88. 19) _ __ A) 4 B) . C) 28 7 D) 7 20) Transportation officials tell us that 80% of drivers wear seat belts while driving. What is the probability that between 656 and 665 drivers in a sample of 850 drivers wear seat belts? A) 0.1075 B) 0.8925 C) 0.0896 D) 0.0179 20) _ __ 21) A certain baseball player hits a home run in 4% of his at-bats. Consider his at-bats as independent events. How many home runs do we expect the baseball player to hit in 650 at-bats? A) 24.96 B) 26 C) 4 D) 654 21) _ __ 22) The Central Limit Theorem states that 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 population from which we are sampling must be normally distributed. C) The sample size must be large (e.g., at least 30). D) The population from which we are sampling must not be normally distributed. 22) _ __ 23) The weight of com chips dispensed into a 15-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 15.5 ounces and a standard deviation of 0.3 ounce. Suppose 400 bags of chips are randomly selected. Find the probability that the mean weight of these 400 bags exceeds 15.6 ounces. B) .6915 A) approximately 0 C) .1915 D) .3085 23) _ __ A-3 24) Which statement best describes a parameter? A) A parameter is a level of confidence associated with an interval about a sample mean or proportion. B) A parameter is a numerical measure of a population that is almost always unknown and must be estimated. C) A parameter is a sample size that guarantees the error in estimation is within acceptable limits. D) A parameter is an unbiased estimate of a statistic found by experimentation or polling. 24) _ __ 25) A 99% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($107,815, $122,881). 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 and increase the confidence level. B) Decrease the sample size and increase the confidence level. C) Decrease the sample size and decrease the confidence level. D) Increase the sample size and decrease the confidence level. 25) _ __ 26) How much money does the average professional football fan spend on food at a single football game? That question was posed to 60 randomly selected football fans. The sampled results show that the sample mean was $70.00 and prior sampling indicated that the population standard deviation was $17.50. Use this information to create a 95 percent confidence interval for the population mean. 0 A) 70 :t 1.64{1:dool B) 70 :t 1.67{1:do 26) 1 C) 70 :t 1.96 17 ,;;o D) 70 :t 1.83 ~~ l~O ~~ 27) An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA - for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). Which of the following statements is true? A) In construction of the confidence interval, at-value with 20 degrees of freedom was used. B) In construction of the confidence interval, a z-value with 20 degrees of freedom was used. C) In construction of the confidence interval, at-value with 19 degrees of freedom was used. D) In construction of the confidence interval, a z-value was used. 27) 28) A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval for the mean was calculated to be ($2,181,260, $5,836,180). What additional assumption is necessary for this confidence interval to be valid? A) The sample standard deviation is less than the degrees of freedom. B) The distribution of the sample means is approximately normal. C) The population of total compensations of CEOs in the service industry is approximately normally distributed. D) None. The Central Limit Theorem applies. 28) _ __ A-4 29) A marketing research company is estimating 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: (.453, .493). Identify the point estimate for estimating the true proportion of college students who prefer that drink. A) .02 B) .493 C) .453 D) .473 29) 30) A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 6.6 hours. In order to test whether the time to fill out the form has been reduced, a sample of 72 small business owners who annually complete the form was randomly chosen, and their completion times recorded. The mean completion time for ABC-5500 form was 6 hours with a standard deviation of 2.6 hours. In order to test that the time to complete the form has been reduced, state the appropriate null and alternative hypotheses. A) Ho : = 6.6 B) Ho: = 6.6 C) Ho: > 6.6 D) Ho: = 6.6 30) _ __ Ha:~6.6 Ha : > 6.6 Ha:<6 .6 Ha : < 6.6 31) Researchers have claimed that the average number of headaches per student during a semester of Statistics is 12. Statistics students believe the average is higher. In a sample of n = 13 students the mean is 16 headaches with a deviation of 1.5. Which of the following represent the null and alternative hypotheses necessary to test the students' belief? A) Ho := 12 vs. Ha: > 12 B) Ho:= 12 VS. Ha : < 12 D) Ho:= 12 vs. Ha : C) Ho: < 12 vs. Ha:= 12 ~ 31) _ __ 12 32) Suppose we wish to test Ho:= 58 vs. Ha:> 58. What will result if we conclude that the mean is greater than 58 when its true value is really 60? A) a Type II error B) a correct decision C) a Type I error D) none of the above 32) _ __ 33) Consider the following printout. 33) _ _ HYPOTHESIS: VARIANCE X = x X = gpa SAMPLE MEAN OF X = SAMPLE VARIANCE OF X = SAMPLE SIZE OF X = HYPOTHESIZED VALUE (x) = 2.4796 .25000 219 2.6 VARIANCE X - x = -.1204 z = -3.56351 State the proper conclusion when testing Ho:= 2.6 vs. Ha:< 2.6 at a= .05. A) Accept Ho. B) Reject Ho. C) Fail to reject Ho. D) We cannot determine from the information given. A-5 34) A bottling company produces bottles that hold 12 ounces of liquid. 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 bottles is 11.9155 ounces with a standard deviation of 0.40 ounce. Suppose the p-value of this test is 0.0455. State the proper conclusion. A) At a = 0.025, reject the null hypothesis. B) At a= 0.10, fail to reject the null hypothesis. C) At a= 0.05, reject the null hypothesis. D) At a= 0.05, accept the null hypothesis. 34) _ __ 35) A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of n = 22 cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. Find a rejection region appropriate for this test if we are using a = 0.05. A) Reject Ho if t > 1.721 B) Reject Ho if t > 1.725 C) Reject Ho if t > 2.080 or t < -2.080 D) Reject Ho if t > 1.717 35) _ __ 36) A paired difference experiment yielded nd pairs of observations. For the given case, what is the 36) _ __ rejection region for testing Ho: d = 9 against Ha: d > 9? nd = 19, a= 0.01 A) t > 2.552 B) t > 2.539 C) t < 2.861 D) t < 2.552 37) Online classes are becoming more and more prevalent at the college level. A statistics instructor randomly sampled ten students from his traditional face-to-face class and ten students from his online class to compare their comprehension of the material that was taught in the class. He administered the same final exam to each student and wants to use the Wilcoxon Rank Sum test to compare their exam scores. The results are shown below: Traditional Class 82 91 75 68 93 85 74 70 56 82 Online Class 67 66 72 73 77 76 48 81 86 92 What alternative hypothesis should the instructor test to show that the students in the traditional class outperformed the students in the online class? A) The distribution of exams scores for the traditional class is shifted to the left of the distribution of exams scores for the online class. B) The distribution of exams scores for the traditional class is shifted to the right or to the left of the distribution of exams scores for the online class. C) The distribution of exams scores for the traditional class is identical to the distribution of exams scores for the online class. D) The distribution of exams scores for the traditional class is shifted to the right of the distribution of exams scores for the online class. A-6 37) _ __ 38) A cola manufacturer invited consumers to take a blind taste test. Consumers were asked to decide which of two sodas they preferred. The manufacturer was also interested in what factors played a role in taste preferences. Below is a printout comparing the taste preferences of men and women. 38) _ __ HYPOTHESIS: PROP. X =PROP. Y SAMPLES SELECTED FROM soda(brandl,brand2) males females (NUMBER= 115) (NUMBER= 56) (sex=O, males) (sex=l, females) X =males Y =females SAMPLE PROPORTION OF X = 0.422018 SAMPLE SIZE OF X = 109 SAMPLE PROPORTION OF Y = 0.25 SAMPLE SIZE OF Y = 52 PROPORTION X - PROPORTION Y = z= 0.172018 2.11825 Suppose the manufacturer wanted to test to determine if the males preferred its brand more than the females. Using the test statistic given, compute the appropriate p-value for the test. A) .4681 B) .0170 C) .2119 D) .0340 39) 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 were each asked if they would be willing to give blood when called by a local hospital. A success is defined as a person who responds to the call and donates blood. The goal is to compare the percentage of the successes of the male and female responses. Find the rejection region that would be used if it is desired to test to determine if a difference exists between the proportion of the females and males who responds to the call to donate blood. Use a= 0.10. A) Reject Ho if z > 1.645. B) Reject Ho if z < -1.645 or z > 1.645. C) Reject Ho if z < -1.96 or z > 1.96. D) Reject Ho if z < -1.96. A-7 39) 40) 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 linear regression model: 40) _ __ E(y) = ~o +~ix, where y =appraised value of the house (in thousands of dollars) and x =number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following result was obtained: /\\ y = 74.80 + i9.72x Which of the following statements concerning the deterministic model, E(y) = ~O A) All of the above statements are true. +~ix is true? /\\ B) A plot of the predicted appraised values y against the number of rooms x for the sample of houses in East Meadow would not result in a straight line. C) In theory, if the appraised values y and number of rooms x for the entire population of houses in East Meadow were obtained and the (x, y) data points plotted, the points would fall in a straight line. D) In theory, a plot of the mean appraised value E(y) against the number of rooms x for the entire population of houses in east Meadow would result in a straight line. 4i) Is there a relationship between the raises administrators at County University receive and their performance on the job? 4i) A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the linear regression model E(y) = ~o +~ix. The faculty group obtained the following prediction equation: /\\ y = i4,000 - 2,000x Which of the following statements about the model E(y) = ~O +~ix is correct? A) The model hypothesizes a line of means; as rating (x) increases, the mean raise E(y) moves up or down along a straight line. B) The model hypothesizes that, on average, administrators make more money than professors. C) The model hypothesizes that the raises for the administrators fall in a perfect straight line. D) The model hypothesizes that knowing an administrator's rating (x) will determine exactly the administrator's raise (y). 42) Consider the data set shown below. Find the estimate of the slope of the least squares regression line. yl013121318110111 x -2 0 2 4 6 8 10 A) 0.94643 C) 1.5 B) 0.9003 A-8 D) 1.49045 42) 43) Consider the data set shown below. Find the estimate of they-intercept of the least squares regression line. 43) - - - yl013121318110111 x -2 0 2 4 6 8 10 A) 1.5 B) 1.49045 C) 0.94643 0) 0.9003 44) 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) = /30 + f31x, where y =appraised value of the house (in thousands of dollars) and x =number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following results were obtained: I\\ y = 74.80 + 20.74x 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 20.74. B) For a house with 0 rooms, we estimate the appraised value to be $74,800. C) For each additional room in the house, we estimate the appraised value to increase $74,800. D) For each additional room in the house, we estimate the appraised value to increase $20,740. A-9 44) 45) 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: PRESSURE: 45) _ __ y =Number of man-hours required to erect the drum x 1= Boiler design pressure (pounds per square inch, i.e., psi) The simple linear model E(y) = ~O + ~lX was fit to the data. A printout for the analysis appears below: UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF MANHRS PREDICTOR VARIABLES CONSTANT PRESSURE COEFFICIENT 1.88059 0.00321 R-SQUARED ADJUSTED R-SQUARED SOURCE REGRESSION RESIDUAL TOTAL OF 1 34 35 0.4342 0.4176 SS 111.008 144.656 255.665 STD ERROR 0.58380 0.00163 p STUDENT'ST 3.22 2.17 0.0028 0.0300 RESID. MEAN SQUARE (MSE) STANDARD DEVIATION 4.25460 2.06267 MS 111.008 4.25160 F 5.19 p 0.0300 Fill in the blank. At a =.01, there is between man-hours and pressure. A) insufficient evidence of a positive linear relationship B) sufficient evidence of a negative linear relationship C) sufficient evidence of a linear relationship D) sufficient evidence of a positive linear relationship 46) An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using 25 data points is shown below. /\\ /\\ ~o = -92040 ~1 = 228 s = 3213 r2 = .66 r = .81 df = 23 t = 6.67 Give a practical interpretation of r = .81. A) We estimate SALARY to increase 81% for every 1-point increase in 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) There appears to be a positive correlation between SALARY and GMAT. A-10 46) _ __ Final Exam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The average age of the students in a statistics class is 22 years. Does this statement describe descriptive or inferential statistics? A) Inferential statistics B) Descriptive statistics 1) 2) A study attempted to estimate the proportion of Florida residents who were willing to spend more tax dollars on protecting the Florida beaches from environmental disasters. Forty-three hundred Florida residents were surveyed.Which of the following describes the variable of interest in the study? A) the response to the question "Do you use the beach?" B) the response to the question, "Are you willing to spend more tax dollars on protecting the Florida beaches from environmental disasters?" C) the 4300 Florida residents surveyed D) the response to the question "Do you live along the beach?" 2) 3) As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. Identify the experimental unit of interest for this study. A) the entire set of stocks that are traded on the NYSE B) the 500 NYSE stocks that current prices were collected from C) the current price (or dosing price) of a NYSE stock D) a single stock traded on the NYSE 3) 4) An usher records the number of unoccupied seats in a movie theater during each viewing of a film. Identify the type of data collected. A) qualitative B) quantitative 4) 5) The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 330 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watches television. Identify how the data were collected in this study. A) from a designed experiment B) from a published source C) from a survey D) observationally 5) 6) Because of the possible legal consequences, many people in a sample of the U.S. population chose not to participate in a survey regarding illegal drug use. What type of problem has occurred? A) selection bias B) nonresponse bias C) measurement error 6) B-1 7) A sociologist recently conducted a survey of senior citizens who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows: 67 73 68 62 59 72 60 91 67 86 65 88 75 80 74 75 64 61 69 63 7) _ _ __ 85 89 80 72 81 Find the median of the observations. A) 73 B) 72.5 C)72 0) 69 8) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits 8) during the tournament. The statistician reported that the mean serve speed of a particular player was 104 miles per hour (mph) and the standard deviation of the serve speeds was 15 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) 89 mph to 119 mph B) 134 mph to 164 mph C) 74 mph to 134 mph 0) 59 mph to 149 mph 9) 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 most 25% 0) at least 75% 9) 10) Given a data set, which of the following is most likely to be the percentage of data within three standard deviations of the mean? A) 85% B) 95% C) 70% 0) 65% 10) _ __ 11) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the standard deviation of the expenditures was calculated to be $100. Suppose a randomly selected student reported that their textbook expenditure was $700. Calculate the z-score for this student's textbook expenditure. A) +2 B) -3 . C) +3 0) -2 11) 12) An experiment consists of rolling two dice and summing the resulting values. Which of the following is not a sample point for this experiment? A)2 B)7 C)l 0)6 12) 13) Two chips are drawn at random and without replacement from a bag containing four blue chips and three red chips. Find the probability of drawing two red chips. 13) _ __ ~l 7 ~~ C)~ 49 12 ~! 7 Compute. 14) - - - 14)UJ A) 35 C) 24 B) 210 B-2 0)2 Solve the problem. 15) Suppose that for a certain experiment P(A) = .47 and P(B) = .25 and P(A n B) = .14. Find P(A u B). A) .86 B) .58 C) .36 D) .72 15) _ __ 16) 16) Use the standard normal distribution to find P(-2.25 < z < 1.25). A) .8821 B) .4878 C) .0122 D) .8944 17) Use the standard normal distribution to find P(z < -2.33 or z > 2.33). A) .0606 B) .9809 C) .7888 D) .0198 17) _ _ 18) 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 1100 miles. What is the probability a certain tire of this brand will last between 57,690 miles and 58,020 miles? A) .4920 B) .0180 C) .9813 D) .4649 18) _ __ 19) Suppose a random variable xis best described by a normal distribution with= 60anda=10. Find the z-score that corresponds to the value x = 100. 19) _ __ A) 40 B) ~ C) 4 2 D) 10 20) Transportation officials tell us that 60% of drivers wear seat belts while driving. What is the probability that between 509 and 521 drivers in a sample of 900 drivers wear seat belts? A) 0.0162 B) 0.8962 C) 0.0876 D) 0.1038 20) _ __ 21) A certain baseball player hits a home run in 8% of his at-bats. Consider his at-bats as independent events. How many home runs do we expect the baseball player to hit in 850 at-bats? A) 858 B) 68 C) 62.56 D) 8 21) _ __ 22) The Central Limit Theorem states that 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 from which we are sampling must not be normally distributed. B) The population size must be large (e.g., at least 30). C) The population from which we are sampling must be normally distributed. D) The sample size must be large (e.g., at least 30). 22) _ __ 23) The weight of com chips dispensed into a 20-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 20.5 ounces and a standard deviation of 0.1 ounce. Suppose 400 bags of chips are randomly selected. Find the probability that the mean weight of these 400 bags exceeds 20.6 ounces. B) .1915 A) .6915 C) .3085 D) approximately 0 23) B-3 24) Which statement best describes a parameter? A) A parameter is a sample size that guarantees the error in estimation is within acceptable limits. B) A parameter is a level of confidence associated with an interval about a sample mean or proportion. C) A parameter is a numerical measure of a population that is almost always unknown and must be estimated. D) A parameter is an unbiased estimate of a statistic found by experimentation or polling. 24) _ __ 25) A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($91,623, $104,880). 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 increase 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 decrease the confidence level. 25) _ __ 26) How much money does the average professional football fan spend on food at a single football game? That question was posed to 60 randomly selected football fans. The sampled results show that the sample mean was $70.00 and prior sampling indicated that the population standard deviation was $17.50. Use this information to create a 95 percent confidence interval for the population mean. 0 70 83 A) i. B) 70 1.96c{ 26) 3[ $ool C) 70 1.67{ ~ D) 70 d .641 $o 1 $o 27) An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GP A - for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). Which of the following statements is true? A) In construction of the confidence interval, at-value with 19 degrees of freedom was used. B) In construction of the confidence interval, a z-value was used. C) In construction of the confidence interval, at-value with 20 degrees of freedom was used. D) In construction of the confidence interval, a z-value with 20 degrees of freedom was used. 27) 28) A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 99% confidence interval for the mean was calculated to be ($2,181,260, $5,836,180). What additional assumption is necessary for this confidence interval to be valid? A) The distribution of the sample means is approximately normal. B) The population of total compensations of CEOs in the service industry is approximately normally distributed. C) None. The Central Limit Theorem applies. D) The sample standard deviation is less than the degrees of freedom. 28) _ __ B-4 29) A marketing research company is estimating 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: (.352, .512). Identify the point estimate for estimating the true proportion of college students who prefer that drink. B) .512 C) .352 0) .08 A) .432 29) 30) A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 6.7 hours. In order to test whether the time to fill out the form has been reduced, a sample of 36 small business owners who annually complete the form was randomly chosen, and their completion times recorded. The mean completion time for ABC-5500 form was 6 hours with a standard deviation of 1.9 hours. In order to test that the time to complete the form has been reduced, state the appropriate null and alternative hypotheses. A) Ho : > 6.7 B) Ho: = 6.7 C) Ho:= 6.7 0) Ho : = 6.7 Ha: < 6.7 Ha:<6 .7 ha :> 6.7 30) 31) Researchers have claimed that the average number of headaches per student during a semester of Statistics is 16. Statistics students believe the average is higher. In a sample of n = 13 students the mean is 18 headaches with a deviation of 1.6. Which of the following represent the null and alternative hypotheses necessary to test the students' belief? B) Ho:< 16 vs. Ha:= 16 A) Ho : = 16 vs. Ha : < 16 C) Ho:= 16 vs. Ha : ~ 16 D) Ho:= 16 vs. Ha : > 16 31) _ __ 32) Suppose we wish to test Ho : = 53 vs. Ha : > 53. What will result if we conclude that the mean is greater than 53 when its true value is really 60? A) a Type II error B) a Type I error C) a correct decision 0) none of the above 32) _ __ 33) Consider the following printout. 33) - - - HYPOTHESIS: VARIANCE X = x X = SAMPLE MEAN OF X = SAMPLE VARIANCE OF X = SAMPLE SIZE OF X = HYPOTHESIZED VALUE (x) = gpa 2.4815 .18000 201 2.6 VARIANCE X - x = -.1185 z = -3 .95986 State the proper conclusion when testing Ho:= 2.6 vs. Ha : < 2.6 at a= .05. A) Fail to reject Ho. B) Accept Ho . C) Reject Ho. 0) We cannot determine from the information given. B-5 34) A bottling company produces bottles that hold 12 o~ce~ of liquid. P~riod~cally, the co~pany gets complaints that their bottles are not holding enough liqUid. To ~est.this claim, the bottlin~ company randomly samples 49 bottles and finds the average amount of liqUid held ~y the ~ottles is 11.9145 ounces with a standard deviation of 0.35 ounce. Suppose the p-value of this test is 0.0436. State the 34) - - - proper conclusion. A) At a= 0.10, fail to reject the null hypothesis. B) At a = 0.025, reject the null hypothesis. C) At a = 0.05, reject the null hypothesis. D) At a = 0.05, accept the null hypothesis. 35) A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of n = 22 cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. Find a rejection region appropriate for this test if we are using a= 0.05. A) Reject Ho if t > 1.717 B) Reject Ho if t > 1.721 C) Reject Ho if t > 2.080 or t < -2.080 D) Reject Ho if t > 1.725 36) A paired difference experiment yielded nd pairs of observations. For the given case, what is the rejection region for testing Ho: d nd = 6, a= 0.025 A) t > 2.571 = 36) _ __ 9 against Ha: d > 9? C) t < 2.571 B) t > 2.447 D) t < 2.015 37) Online classes are becoming more and more prevalent at the college level. A statistics instructor randomly sampled ten students from his traditional face-to-face class and ten students from his online class to compare their comprehension of the material that was taught in the class. He administered the same final exam to each student and wants to use the Wilcoxon Rank Sum test to compare their exam scores. The results are shown below: Traditional Class 82 91 75 68 93 85 74 70 56 82 35) Online Class 67 66 72 73 77 76 48 81 86 92 What alternative hypothesis should the instructor test to show that the students in the traditional class outperformed the students in the online class? A) The distribution of exams scores for the traditional class is shifted to the right of the distribution of exams scores for the online class. B) The distribution of exams scores for the traditional class is identical to the distribution of exams scores for the online class. C) The distribution of exams scores for the traditional class is shifted to the right or to the left of the distribution of exams scores for the online class. D) The distribution of exams scores for the traditional class is shifted to the left of the distribution of exams scores for the online class. B-6 37) 38) A cola manufacturer invited consumers to take a blind taste test. Consumers were asked to decide which of two sodas they preferred. The manufacturer was also interested in what factors played a role in taste preferences. Below is a printout comparing the taste preferences of men and women. 38) _ __ HYPOTHESIS: PROP. X =PROP. Y SAMPLES SELECTED FROM soda(brandl,brand2) males females (NUMBER = 115) (NUMBER= 56) (sex=O, males) (sex=l, females) X =males Y =females SAMPLE PROPORTION OF X = 0.422018 SAMPLE SIZE OF X = 109 SAMPLE PROPORTION OF Y = 0.25 SAMPLE SIZE OF Y = 52 PROPORTION X - PROPORTION Y = z= 0.172018 2.11825 Suppose the manufacturer wanted to test to determine if the males preferred its brand more than the females. Using the test statistic given, compute the appropriate p-value for the test. A) .2119 B) .4681 C) .0170 D) .0340 39) 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 were each asked if they would be willing to give blood when called by a local hospital. A success is defined as a person who responds to the call and donates blood. The goal is to compare the percentage of the successes of the male and female responses. Find the rejection region that would be used if it is desired to test to determine if a difference exists between the proportion of the females and males who responds to the call to donate blood. Use a= 0.10. A) Reject Ho if z > 1.645. B) Reject Ho if z < -1.645 or z > 1.645. C) Reject Ho if z < -1.96. D) Reject Ho if z < -1.96 or z > 1.96. B-7 39) 40) 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 linear regression model: 40) _ __ E(y) = ~o +~I x, where y =appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following result was obtained: /\\ y = 74.80 + I9.72x Which of the following statements concerning the deterministic model, E(y) = ~O +~IX is true? A) In theory, if the appraised values y and number of rooms x for the entire population of houses in East Meadow were obtained and the (x , y) data points plotted, the points would fall in a straight line. B) All of the above statements are true. /\\ C) A plot of the predicted appraised values y against the number of rooms x for the sample of houses in East Meadow would not result in a straight line. D) In theory, a plot of the mean appraised value E(y) against the number of rooms x for the entire population of houses in east Meadow would result in a straight line. 4I) Is there a relationship between the raises administrators at County University receive and their performance on the job? 4I) _ __ A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the linear regression model The faculty group obtained the following prediction equation: /\\ y = I4,000 - 2,000x Which of the following statements about the model E(y) = ~O +~IX is correct? A) The model hypothesizes that the raises for the administrators fall in a perfect straight line. B) The model hypothesizes a line of means; as rating (x) increases, the mean raise E(y) moves up or down along a straight line. C) The model hypothesizes that, on average, administrators make more money than professors. D) The model hypothesizes that knowing an administrator's rating (x) will determine exactly the administrator's raise (y). 42) Consider the data set shown below. Find the estimate of the slope of the least squares regression line. y l013121318110111 x -2 0 2 4 6 8 10 A) 0.94643 B) 1.49045 C) I.5 B-8 D) 0.9003 42) --- 43) Consider the data set shown below. Find the estimate of they-intercept of the least squares regression line. 43) - - - yl013121318110111 x -2 0 2 4 6 8 10 A) 1.49045 B) 1.5 C) 0.9003 D) 0.94643 44) 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) = ~O + ~p, where y =appraised value of the house (in thousands of dollars) 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 + 21.9lx 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 21.91. B) For each additional room in the house, we estimate the appraised value to increase $74,800. C) For a house with 0 rooms, we estimate the appraised value to be $74,800. D) For each additional room in the house, we estimate the appraised value to increase $21,910. B-9 44) 45) 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: PRESSURE: 45) _ __ y =Number of man-hours required to erect the drum x1 =Boiler design pressure (pounds per square inch, i.e., psi) The simple linear model E(y) = ~O +~I X was fit to the data. A printout for the analysis appears below: UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF MANHRS PREDICTOR VARIABLES CONSTANT PRESSURE COEFFICIENT 1.88059 0.00321 R-SQUARED ADJUSTED R-SQUARED SOURCE REGRESSION RESIDUAL TOTAL OF 1 34 35 0.4342 0.4176 SS 111.008 144.656 255.665 STD ERROR 0.58380 0.00163 p STUDENT'ST 3.22 2.17 0.0028 0.0300 RESID. MEAN SQUARE (MSE) STANDARD DEVIATION 4.25460 2.06267 MS 111.008 4.25160 F 5.19 p 0.0300 Fill in the blank. At a =.01, there is between man-hours and pressure. A) sufficient evidence of a positive linear relationship B) sufficient evidence of a linear relationship C) insufficient evidence of a positive linear relationship D) sufficient evidence of a negative linear relationship 46) An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMA T score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using 25 data points is shown below. f\\ f\\ ~O = -92040 ~1 = 228 s = 3213 r2 = .66 r = .81 df = 23 t = 6.67 Give a practical interpretation of r = .81. A) 81 % of the sample variation in SALARY can be explained by using GMAT in a straight-line model. B) We estimate SALARY to increase 81 % for every 1-point increase in GMAT. C) There appears to be a positive correlation between SALARY and GMA T. D) We can predict SALARY correctly 81% of the time using GMAT in a straight-line model. B-10 46) _ __ Final Exam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The average age of the students in a statistics class is 22 years. Does this statement describe descriptive or inferential statistics? A) Descriptive statistics B) Inferential statistics 1) 2) A study attempted to estimate the proportion of Florida residents who were willing to spend more tax dollars on protecting the Florida beaches from environmental disasters. Forty-eight hundred Florida residents were surveyed.Which of the following describes the variable of interest in the study? A) the 4800 Florida residents surveyed B) the response to the question "Do you use the beach?" C) the response to the question, "Are you willing to spend more tax dollars on protecting the Florida beaches from environmental disasters?" D) the response to the question "Do you live along the beach?" 2) 3) As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. Identify the experimental unit of interest for this study. A) the 500 NYSE stocks that current prices were collected from B) the current price (or closing price) of a NYSE stock C) a single stock traded on the NYSE D) the entire set of stocks that are traded on the NYSE 3) 4) An usher records the number of unoccupied seats in a movie theater during each viewing of a film . Identify the type of data collected. A) quantitative B) qualitative 4) 5) The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PA WT). 330 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watches television. Identify how the data were collected in this study. A) from a published source B) observationally C) from a designed experiment D) from a survey 5) 6) Because of the possible legal consequences, many people in a sample of the U.S. population chose not to participate in a survey regarding illegal drug use. What type of problem has occurred? A) measurement error B) nonresponse bias C) selection bias 6) C-1 7) A sociologist recently conducted a survey of senior citizens who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows: 70 76 71 65 62 75 63 94 70 89 68 91 78 83 77 78 67 64 72 66 7) _ _ __ 88 92 83 75 84 Find the median of the observations. B) 75 A) 72 C) 76 D) 75.5 8) 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 12 mph. If nothing is known about the shape of the distribution, give an interval that will contain the speeds of at least eight-ninths of the player's serves. A) 48 mph to 144 mph B) 132 mph to 168 mph C) 60 mph to 132 mph D) 72 mph to 120 mph 8) _ _ __ 9) If nothing is known about the shape of a distribution, what percentage of the observations fall within 3 standard deviations of the mean? B) at most 11 % A) at least 89% C) approximately 99.7% D) approximately 0.3% 9) 10) Given a data set, which of the following is most likely to be the percentage of data within three standard deviations of the mean? A) 95% B) 70% C) 85% D) 65% 10) 11) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the standard deviation of the expenditures was calculated to be $100. Suppose a randomly selected student reported that their textbook expenditure was $700. Calculate the z-score for this student's textbook expenditure. A) -2 B) +3 C) -3 D) +2 11) 12) An experiment consists of rolling two dice and summing the resulting values. Which of the following is not a sample point for this experiment? 12) _ __ A)7 B)l C)6 D)2 13) Two chips are drawn at random and without replacement from a bag containing four blue chips and three red chips. Find the probability of drawing two red chips. ~! 7 ~~ q! 7 49 13) _ __ ~~ 12 Compute. 14) ( ~J A) 56 14) - - C) 336 B) 3 C-2 D) 120 Solve the problem. 15) Suppose that for a certain experiment P(A) = .47 and P(B) = .25 and P(A n B) = .14. Find P(A u B). ~ .~ ~.~ C) .n D).~ 16) Use the standard normal distribution to find P(-2.25 < z < 1.25). A) .4878 B) .8821 C) .0122 D) .8944 17) Use the standard normal distribution to find P(z < -2.33 or z > 2.33). A) .7888 B) .0198 C) .9809 15) _ __ D) .0606 16) 17) _ _ 18) 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 2400 miles. What is the probability a certain tire of this brand will last between 54,960 miles and 55,680 miles? A) .0180 B) .4920 C) .9813 D) .4649 18) 19) Suppose a random variable xis best described by a normal distribution with= 60 and a= 8. Find the z-score that corresponds to the value x = 92. 19) A)4 C) 8 B) 32 20) Transportation officials tell us that 90% of drivers wear seat belts while driving. What is the probability that between 525 and 530 drivers in a sample of 600 drivers wear seat belts? A) 0.0985 B) 0.0174 C) 0.9015 D) 0.0811 20) 21) A certain baseball player hits a home run in 4% of his at-bats. Consider his at-bats as independent events. How many home runs do we expect the baseball player to hit in 650 at-bats? A) 4 B) 26 C) 654 D) 24.96 21) 22) The Central Limit Theorem states that 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 sample size must be large (e.g., at least 30). B) The population from which we are sampling must not be normally distributed. C) The population from which we are sampling must be normally distributed. D) The population size must be large (e.g., at least 30). 22) 23) The weight of com chips dispensed into a 12-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 12.5 ounces and a standard deviation of 0.3 ounce. Suppose 100 bags of chips are randomly selected. Find the probability that the mean weight of these 100 bags exceeds 12.6 ounces. A) approximately 0 B) .1915 C) .6915 D) .3085 23) _ __ C-3 24) Which statement best describes a parameter? A) A parameter is a sample size that guarantees the error in estimation is within acceptable limits. B) A parameter is a numerical measure of a population that is almost always unknown and must be estimated. C) A parameter is a level of confidence associated with an interval about a sample mean or proportion. D) A parameter is an unbiased estimate of a statistic found by experimentation or polling. 24) 25) A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($137,351, $147,668). 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) Decrease the sample size and increase the confidence level. C) Increase the sample size and decrease the confidence level. D) Increase the sample size and increase the confidence level. 25) 26) How much money does the average professional football fan spend on food at a single football game? That question was posed to 60 randomly selected football fans. The sampled results show that the sample mean was $70.00 and prior sampling indicated that the population standard deviation was $17.50. Use this information to create a 95 percent confidence interval for the population mean. 0 A) 7o 1.67{$ool B) 70 1.83{$o 26) _ __ 1 C) 70 1.64 17 ~0 D) 70 1.96 ~~ l~O ~~ 27) An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA- for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). Which of the following statements is true? A) In construction of the confidence interval, a z-value with 20 degrees of freedom was used. B) In construction of the confidence interval, at-value with 19 degrees of freedom was used. C) In construction of the confidence interval, a z-value was used. D) In construction of the confidence interval, a t-value with 20 degrees of freedom was used. 27) _ __ 28) A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 90% confidence interval for the mean was calculated to be ($2,181,260, $5,836,180). What additional assumption is necessary for this confidence interval to be valid? A) The sample standard deviation is less than the degrees of freedom. B) The population of total compensations of CEOs in the service industry is approximately normally distributed. C) None. The Central Limit Theorem applies. D) The distribution of the sample means is approximately normal. 28) C-4 29) A marketing research company is estimating 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: (.401, .461). Identify the point estimate for estimating the true proportion of college students who prefer that drink. A) .03 B) .401 C) .431 D) .461 29) 30) A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 6.2 hours. In order to test whether the time to fill out the form has been reduced, a sample of 100 small business owners who annually complete the form was randomly chosen, and their completion times recorded. The mean completion time for ABC-5500 form was 6 hours with a standard deviation of 1.9 hours. In order to test that the time to complete the form has been reduced, state the appropriate null and alternative hypotheses. A) Ho: = 6.2 B) Ho: = 6.2 C) Ho:> 6.2 D) Ho : = 6.2 Ha: ;e 6.2 Ha: >6.2 Ha: < 6.2 Ha : < 6.2 30) _ __ 31) Researchers have claimed that the average number of headaches per student during a semester of Statistics is 15. Statistics students believe the average is higher. In a sample of n = 24 students the mean is 16 headaches with a deviation of 2. Which of the following represent the null and alternative hypotheses necessary to test the students' belief? A) Ho : = 15 vs. Ha: ;C 15 B) Ho:= 15 vs. Ha: > 15 31) _ __ C) Ho : < 15 vs. Ha : = 15 D) Ho:= 15 vs. Ha: < 15 32) Suppose we wish to test Ho : = 60 vs. Ha:> 60. What will result if we conclude that the mean is greater than 60 when its true value is really 68? A) a correct decision B) a Type II error C) a Type I error D) none of the above 32) _ __ 33) Consider the following printout. 33) - - - HYPOTHESIS: VARIANCE X = x X = gpa SAMPLE MEAN OF X = SAMPLE VARIANCE OF X = SAMPLE SIZE OF X = HYPOTHESIZED VALUE (x) = 2.2667 .18000 229 2.4 VARIANCE X - x = -.1333 z = -4.75457 State the proper conclusion when testing Ho : = 2.4 vs. Ha: < 2.4 at a= .05. A) Fail to reject Ho. B) Reject Ho. C) Accept Ho . D) We cannot determine from the information given. C-5 34) A bottling company produces bottles that hold 8 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 36 bottles and finds the average amount of liquid held by the bottles is 7.9145 ounces with a standard deviation of 0.30 ounce. Suppose the p-value of this test is 0.0436. State the proper conclusion. A) At a = 0.025, reject the null hypothesis. B) At a = 0.05, accept the null hypothesis. C) At a= 0.10, fail to reject the null hypothesis. D) At a = 0.05, reject the null hypothesis. 34) 35) A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of n = 22 cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. Find a rejection region appropriate for this test if we are using a = 0.05. A) Reject Ho if t > 1.725 B) Reject Ho if t > 2.080 or t < -2.080 D) Reject Ho if t > 1.717 C) Reject Ho if t > 1.721 35) 36) A paired difference experiment yielded nd pairs of observations. For the given case, what is the 36) _ __ rejection region for testing Ho: d = 9 against Ha: d > 9? nd = 8, a= 0.1 A) t < 1.895 B) t > 1.397 C) t > 1.415 D) t < 1.415 37) Online classes are becoming more and more prevalent at the college level. A statistics instructor randomly sampled ten students from his traditional face-to-face class and ten students from his online class to compare their comprehension of the material that was taught in the class. He administered the same final exam to each student and wants to use the Wilcoxon Rank Sum test to compare their exam scores. The results are shown below: Traditional Class 82 91 75 68 93 85 74 70 56 82 Online Class 67 66 72 73 77 76 48 81 86 92 What alternative hypothesis should the instructor test to show that the students in the traditional class outperformed the students in the online class? A) The distribution of exams scores for the traditional class is shifted to the right or to the left of the distribution of exams scores for the online class. B) The distribution of exams scores for the traditional class is shifted to the left of the distribution of exams scores for the online class. C) The distribution of exams scores for the traditional class is identical to the distribution of exams scores for the online class. D) The distribution of exams scores for the traditional class is shifted to the right of the distribution of exams scores for the online class. C-6 37) 38) A cola manufacturer invited consumers to take a blind taste test. Consumers were asked to decide which of two sodas they preferred. The manufacturer was also interested in what factors played a role in taste preferences. Below is a printout comparing the taste preferences of men and women. 38) HYPOTHESIS: PROP. X =PROP. Y SAMPLES SELECTED FROM soda(brandl,brand2) males females (NUMBER = 115) (NUMBER= 56) (sex=O, males) (sex=l, females) X =males Y =females SAMPLE PROPORTION OF X = 0.422018 SAMPLE SIZE OF X = 109 SAMPLE PROPORTION OF Y = 0.25 SAMPLE SIZE OF Y = 52 PROPORTION X - PROPORTION Y = z= 0.172018 2.11825 Suppose the manufacturer wanted to test to determine if the males preferred its brand more than the females. Using the test statistic given, compute the appropriate p-value for the test. A) .4681 B) .0340 C) .0170 D) .2119 39) 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 were each asked if they would be willing to give blood when called by a local hospital. A success is defined as a person who responds to the call and donates blood. The goal is to compare the percentage of the successes of the male and female responses. Find the rejection region that would be used if it is desired to test to determine if a difference exists between the proportion of the females and males who responds to the call to donate blood. Use a= 0.10. A) Reject Ho if z > 1.645. B) Reject Ho if z < -1.645 or z > 1.645. C) Reject Ho if z < -1.96 or z > 1.96. D) Reject Ho if z < -1.96. C-7 39) _ __ 40) 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 linear regression model: 40) _ __ E(y) = ~O +~IX, where y =appraised value of the house (in thousands of dollars) and x =number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following result was obtained: I\\ y = 74.80 + 19.72x Which of the following statements concerning the deterministic model, E(y) = ~O +~IX is true? A) All of the above statements are true. B) In theory, if the appraised values y and number of rooms x for the entire population of houses in East Meadow were obtained and the (x, y) data points plotted, the points would fall in a straight line. C) In theory, a plot of the mean appraised value E(y) against the number of rooms x for the entire population of houses in east Meadow would result in a straight line. I\\ D) A plot of the predicted appraised values y against the number of rooms x for the sample of houses in East Meadow would not result in a straight line. 41) Is there a relationship between the raises administrators at County University receive and their performance on the job? 41) _ __ A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the linear regression model The faculty group obtained the following prediction equation: I\\ y = 14,000 - 2,000x Which of the following statements about the model E(y) = ~O + ~lX is correct? A) The model hypothesizes that the raises for the administrators fall in a perfect straight line. B) The model hypothesizes that knowing an administrator's rating (x) will determine exactly the administrator's raise (y). C) The model hypothesizes a line of means; as rating (x) increases, the mean raise E(y) moves up or down along a straight line. D) The model hypothesizes that, on average, administrators make more money than professors. 42) Consider the data set shown below. Find the estimate of the slope of the least squares regression line. yl013121318110111 x -2 0 2 4 6 8 10 A) 1.5 B) 1.49045 C) 0.94643 C-8 D) 0.9003 42) --- 43) Consider the data set shown below. Find the estimate of they-intercept of the least squares regression line. 43) - - - YI 013121318110111 x -2 0 2 4 6 8 10 A) 1.49045 C) 1.5 B) 0.9003 D) 0.94643 44) 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: E0f) = ~o +~ix, where y =appraised value of the house (in thousands of dollars) 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 + 24.82x Give a practical interpretation of the estimate of the slope of the least squares line. A) For each additional room in the house, we estimate the appraised value to increase $24,820. B) For each additional dollar of appraised value, we estimate the number of rooms in the house to increase by 24.82. C) For each additional room in the house, we estimate the appraised value to increase $74,800. D) For a house with 0 rooms, we estimate the appraised value to be $74,800. C-9 44) _ __ 45) 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: PRESSURE: 45) y =Number of man-hours required to erect the drum x1 = Boiler design pressure (pounds per square inch, i.e., psi) The simple linear model E(y) = fio + fiix was fit to the data. A printout for the analysis appears below: UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF MANHRS PREDICTOR VARIABLES CONSTANT PRESSURE COEFFICIENT 1.88059 0.00321 R-SQUARED ADJUSTED R-SQUARED SOURCE REGRESSION RESIDUAL TOTAL OF 1 34 35 0.4342 0.4176 SS 111.008 144.656 255.665 p STUDENT'ST 3.22 2.17 0.0028 0.0300 RESID. MEAN SQUARE (MSE) STANDARD DEVIATION 4.25460 2.06267 STD ERROR 0.58380 0.00163 MS 111.008 4.25160 F 5.19 p 0.0300 Fill in the blank. At a =.01, there is between man-hours and pressure. A) sufficient evidence of a positi