Decision Sciences & MIS Department Drexel University March 18th, 2020 STAT201-001 Final Winter 2019-2020 NAME (Print):___Nakhi Finch________________ SIGNATURE: _____________________________ STUDENT IDENTIFICATION NUMBER: _________________ VERSION AA This test consists of 25 multiple-choice questions. Each question has only one correct answer. Read all questions carefully. Some questions are more difficult than others, but all count equally. If you have difficulty with a particular question, it would probably be a good idea to move on to other questions and return to the difficult question later. In order to receive full credit for your response, you must show all of your work. Good Luck and Have a Safe and Happy Spring Break!!!!! Problems 1 - 25 (100 pts.) Multiple Choices. Choose correct response, and show all your work for Full credit. 1. a) b) c) d) e) A popular restaurant takes a random sample n = 25 customers and records how long each occupied a table. The found a sample mean of 1.2 hours and a sample standard deviation of 0.3 hours. Find the 95 percent confidence interval for the mean. 1.2 ± 0.118 1.2 ± 0.124 1.2 ± 0.588 1.2 ± 0.609 1.2 ± 0.099 2. The time it takes to deliver a pizza (from time of phone call to delivery at door) follows a normal distribution with a mean (µ) of 45 minutes and a standard deviation () of 5 minutes. If a pizza store’s policy is, “Orders delivered within one hour or they’re free!”, what percentage of the store’s total delivery orders will be delivered to consumers with charge? a) b) c) d) e) 2.28% 0.13% 49.87% 0.26% 99.87% THE NEXT 2 QUESTIONS (3-4) REFER TO THE FOLLOWING PROBLEM SETTING. During a water shortage a water company sampled residential water meters in order to determine whether the mean daily water consumption exceeds 130 gallons. Records for a sample of 20 meters on a particular day showed a mean of 155 gallons with a standard deviation equal to 45 gallons. It is assumed that the distribution of individual residential water consumption is normal. 3. The null and alternative hypotheses for the relevant test are which of the following? a) b) c) d) e) H0: X ≤ 130 vs. H0: X ≤ 155 vs. H0: µ ≥ 130 vs. H0: µ = 130 vs. H0: µ ≤ 130 vs. 4. The value of the appropriate test statistic and the responding critical region for this test using the significance level (= 0.05 are, respectively a) b) c) d) e) 2.485; 1.729 2.485; 1.645 1.250; ±2.093 4.968; 1.729 ±1.729; 2.093 H1: X > 130 H1: X > 155 H1: µ < 130 H1: µ ≠ 130 H1: µ > 130 5. A small model-airplane motor has three independent starting components: key, wire, and glow plug. All of these must “work” in order for the plane to start. What is the probability that the plane will start if the probability that each component will work is as follows: key (0.98), wire (0.99), and plug (0.95)? a) b) c) d) e) 0.99 0.95 0.92 0.87 0.98 6. In a box of thermostats received by a local heating/cooling company, 3 of the 9 thermostats are defective. An employee randomly selects 2 thermostats to use on his next installation job. What is the probability that at least one defective thermostat will be among the 2 thermostats selected by the employee? a) b) c) d) e) 0.5833 0.4167 0.9167 0.5000 0.0833 THE NEXT 2 QUESTIONS (7-8) REFER TO THE FOLLOWING PROBLEM SETTING. A major textbook publisher has a contract with a printing company. Part of the contract stipulates that no more than 5 percent of the pages should have any type of printing error. 7. Suppose that the company selects a random sample of 400 pages and finds 33 that have an error. If the printer is meeting the standard, what is the probability that a sample would have 33 or more errors? a) b) c) d) e) 0.1245 0.4986 0.0014 0.1250 0.0500 8. As a quality control measure, the publisher periodically selects a random sample of n = 100 pages. Then, depending on the proportion of pages with errors, they either say nothing to the printer or they complain that the quality has slipped. Suppose the publisher wants no more than a 0.10 chance of mistakenly blaming the printer for poor quality, what should the cut-off proportion be? a) b) c) d) e) About 0.05 About 0.0279 About 0.0779 About 0.0221 About 0.10 9. From past experience, the management of a well-known fast food restaurant estimates that the number of weekly customers at a particular location is normally distributed with a mean of 5000 and a standard deviation of 800 customers. 90% of the time, the minimum number of customers exceeds _______. a) b) c) d) e) 4800 6024 3976 5032 4280 10. Thirty percent (30%) of the customers who enter Aunt Hilda's Gourmet Cookie Shop make purchases of cookies. (Seventy percent walk out of the shop without making a purchase). If there are 11 customers in the shop, what is the probability that between 4 and 8 (inclusive) customers will walk out of the shop without making a purchase? a) b) c) d) e) 0.683 0.728 0.791 0.825 0.409 11. The upper and lower limits for a 98% confidence interval for the average family income in a particular country are $35,675 and $40,125. Which of the following is an appropriate interpretation of this confidence interval? Explain your choice. a) b) c) d) e) Only 2% of the families have incomes that are below $35,675 or above $40,125. The probability is 0.98 that a randomly selected family’s income will be between $35,675 and $40,125. Ninety-eight percent of the population means are between $35,675 and $40,125. The probability is 0.98 that all family incomes are between $35,675 and $40,125. Ninety-eight percent of the intervals constructed in this way will include the population mean. 12. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors was selected. Suppose that the test statistic is Zcalc. = – 2.20. Can we conclude that H0 should be rejected at the (a) (= 0.05, (b) (= 0.01 level of significance? a) b) c) d) e) (a) Yes; (b) No We don’t have enough information to conclude. (a) Yes; (b) Yes (a) No; (b) No (a) No; (b) Yes 13. The power of a test is measured by its capability of… (Explain your choice) a) b) c) d) e) Rejecting a null hypothesis that is false. Not rejecting a null hypothesis that is false. Rejecting an alternative hypothesis that is true Rejecting a null hypothesis that is true. Not rejecting a null hypothesis that is true. 14. A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The P-value associated with the test statistic in this problem is approximately equal to: a) b) c) d) e) 0.0013 0.0102 0.0100 0.0051 0.0026 15. Based on the following measurement from a sample size of n = 10, construct a 99% confidence interval for the population mean. (These sample data are believed to come from a normal distribution.): 7.7, 8.6, 8.0, 9.1, 9.9, 8.3, 6.1, 6.8, 7.4, and 9.0. a) b) c) d) e) 8.090 ± 1.335 8.090 ± 0.370 8.090 ± 1.142 8.090 ± 1.017 8.090 ± 1.171 16. All other things being held constant, if the sample size (n) is doubled (so that it becomes 2 times as large as previously), the standard error of the mean will be: a) b) c) d) e) One-fourth (0.25) as large as previously. Two (2) times as large as previously. About 0.7071 times as large as previously. Four (4) times as large as previously. One-half (0.50) as large as previously. 17. Forty percent (40%) of the households in a certain area have at least one compact automobile. A researcher selects a random sample of 96 households. What is the probability that in the sample the proportion of households with at least one compact automobile is less than 0.55? a) b) c) d) e) 0.0013 0.0500 0.9987 0.4987 0.0030 18. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 90% confident in her decision, what conclusion can she make? Justify your choice. a) b) c) d) e) There is sufficient evidence that the mean age of her customers is not over 30. There is not sufficient evidence that the mean age of her customers is less than 30. There is not sufficient evidence that the mean age of her customers is over 30. There is sufficient evidence that the mean age of her customers is over 30. There is not sufficient evidence that the mean age of her customers is not over 30. 19. Which of the following will increase the width of a confidence interval (assuming that everything else remains constant)? Justify your choice. a) b) c) d) e) Decreasing the confidence level Increasing the sample size A decrease in the standard deviation Decreasing the sample size Decreasing the margin of error 20. A manufacturer of light fixtures purchases dimmer switches from a supplier that claims its switches are defective only 4% of the time. Determine the sample size that would be required to estimate the true proportion of defective switches if it is desired that the proportion estimate be within 1.5% of the true proportion, with 99% confidence. a) b) c) d) e) 1941 1137 983 702 391 21. A company is converting its overloaded computer system to a newer system and must rewrite a large number of computer programs for the new system. A sample of 10 programs are rewritten and the linear regression relation between number of man-hours required to rewrite a program (y) and the length of the program measured in number of statements (x) is estimated as ŷ = 2.3 + 0.060X. Other estimates obtained in the regression analysis are: The standard error Se = 1.1, X = 90, and SSXX = 10,000. Ninety-five percent confidence limits for the slope 1 of the regression function are: a) b) c) d) e) 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 2.540 0.110 0.140 0.025 0.011 THE NEXT FOUR QUESTIONS (22-25) ARE TOGETHER: The following data represent the number of feet (in thousands) of corrugated board produced in a day and the number of defective boxes produced in a day, over a randomly selected 7–day period 1 40 40 # Feet # Defects ∑X = 470; 2 ∑X = 33,650; 2 80 42 3 60 45 ∑Y = 276; 4 75 30 5 95 32 2 6 50 42 ∑Y = 11,102; 7 70 45 ∑XY = 18,200 22. Calculate the least squares regression line. a) b) c) d) e) 38.082 – 3.590X 50.038 – 0.158X 85.986 + 2.623X 47.455 – 2.868X 10.354 + 0.736X 23. The standard deviation of observations around the regression line is? a) b) c) d) e) 167.22 Cannot be computed from the information given 5.78 33.41 8.77 24. What is the correlation between the # of feet of corrugated board and the number of defective boxes (produced in a day) and the percentage of total variability in Y that can be explained by the regression model, respectively? a) b) c) d) e) -0.4894; 0.2395 0.2389; -0.4880 0.4880; 0.2389 0.4880; -0.2389 0.2389; 0.4880 25. The (absolute value of the) calculated test statistic used to determine if the slope of the regression line is significantly different from zero at the level of significance ( = 0.025, and the appropriate bound on the P-value, respectively, are? a) b) c) d) e) 1.12; P -value > 0.20 2.71; 0.025 < P -value < 0.05 1.25; P -value > 0.20 4.57; P -value < 0.01 1.25; P -value < 0.10