CHAPTER NINE Statistical Inference: Hypothesis Testing for Single Populations B 1. M Term C E Term Hypothesis testing is derived from the mathematical notion of _______. A. B. C. D. 2. direct proof indirect proof margin of error infinity The first step in testing a hypothesis is to establish _______. A. B. C. D. an not rejectance hypothesis and a rejection hypothesis a power function a null hypothesis and alternative hypothesis an indirect hypothesis 265 266 Test Bank B 3. E Term A A. B. C. D. 4. E App D 5. E App are not mutually exclusive are not collectively exhaustive do not reference a population parameter are established correctly Consider the following null and alternative hypotheses. Ho: 7 Ha: > 7 These hypotheses _______________. A. B. C. D. 6. alternative hypothesis is true. null hypothesis is true errors cannot be made the population parameter of interest is known Consider the following null and alternative hypotheses. Ho: 7 Ha: > 6 These hypotheses _______________. A. B. C. D. E App B In testing hypotheses, the researcher initially assumes that the _______. are not mutually exclusive are not collectively exhaustive do not reference a population parameter are established correctly Consider the following null and alternative hypotheses. Ho: 7 Ha: < 6 These hypotheses _______________. A. B. C. D. are not mutually exclusive are not collectively exhaustive do not reference a population parameter are established correctly Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations A 7. E App C A. B. C. D. 8. E App C 9. E App are not mutually exclusive are not collectively exhaustive do not reference a population parameter are established correctly Consider the following null and alternative hypotheses. Ho: p 0.61 Ha: p > 0.61 These hypotheses _______________. A. B. C. D. 10. are not mutually exclusive are not collectively exhaustive do not reference a population parameter are established correctly Consider the following null and alternative hypotheses. Ho: x 352 Ha: x > 352 These hypotheses _______________. A. B. C. D. E App C Consider the following null and alternative hypotheses. Ho: 78 Ha: < 81 These hypotheses _______________. are not mutually exclusive are not collectively exhaustive do not reference a population parameter are established correctly Consider the following null and alternative hypotheses. Ho: P 0.39 Ha: P > 0.39 These hypotheses _______________. A. B. C. D. are not mutually exclusive are not collectively exhaustive do not reference a population parameter are established correctly 267 268 Test Bank C 11. E App D A. B. C. D. 12. E App D Consider the following null and alternative hypotheses. Ho: S 558 Ha: S < 558 These hypotheses _______________. Consider the following null and alternative hypotheses. Ho: 2 35 Ha: 2 < 35 These hypotheses _______________. A. B. C. D. 13. are not mutually exclusive are not collectively exhaustive do not reference a population parameter are established correctly are not mutually exclusive are not collectively exhaustive do not reference a population parameter are established correctly The region of the distribution in hypothesis testing in which the null hypothesis is rejected is called the _______. E Term A. B. C. D. B The rejection and not rejectance regions are divided by a point called the _______. 14. not rejectance region null region alternative region rejection region E Term A. B. C. D. B The portion of the distribution which is not in the rejection region is called the _______. 15. E Term A. B. C. D. dividing point critical value rejection value not rejectance value tolerable region not rejectance region null region alternative region Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations A 16. The probability of committing a Type I error is called _______. E Term A. B. C. D. A The probability of committing a Type I error is called _______. 17. the level of significance beta the power of the test reliability E Term A. B. C. D. A In statistical hypothesis testing, another name for is _______. 18. 269 E Term A. B. C. D. C When a null hypothesis is rejected, the probability of committing a Type II error is _______. 19. level of significance power beta Type II error probability 0 1- M Term A. B. C. D. B When a true null hypothesis is rejected, the researcher has made a _______. 20. M Term A. B. C. D. C When a false null hypothesis is rejected, the researcher has made a _______. 21. M Term A. B. C. D. Type II error Type I error sampling error powerful error Type II error Type I error correct decision powerful error 270 Test Bank A 22. When a researcher fails to reject a false null hypothesis, a ______ error has been committed. M Term A. B. C. D. C When a researcher fails to reject a null hypothesis, the probability of a Type I error is ________. 23. Type II error Type I error sampling error powerful error 0 1- M Term A. B. C. D. B The probability of committing a Type II error is represented by _______. 24. M Term A. B. C. 1- D. / 2 C Power is equal to _______. 25. M Term A. B. C. D. A Consider the following null and alternative hypotheses. Ho: 67 Ha: > 67 These hypotheses _______________. E App 26. A. B. C. D. 1-if the null hypothesis is true if the null hypothesis is false 1- if the null hypothesis is false if the null hypothesis is true indicate a one-tailed test with a rejection area in the right tail indicate a one-tailed test with a rejection area in the left tail indicate a two-tailed test are established incorrectly Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations B 27. E App C A. B. C. D. 28. E App A 29. E App indicate a one-tailed test with a rejection area in the right tail indicate a one-tailed test with a rejection area in the left tail indicate a two-tailed test are established incorrectly Consider the following null and alternative hypotheses. Ho: P 0.16 Ha: P > 0.16 These hypotheses _______________. A. B. C. D. 30. indicate a one-tailed test with a rejection area in the right tail indicate a one-tailed test with a rejection area in the left tail indicate a two-tailed test are established incorrectly Consider the following null and alternative hypotheses. Ho: = 67 Ha: 67 These hypotheses _______________. A. B. C. D. E App B Consider the following null and alternative hypotheses. Ho: 67 Ha: < 67 These hypotheses _______________. indicate a one-tailed test with a rejection area in the right tail indicate a one-tailed test with a rejection area in the left tail indicate a two-tailed test are established incorrectly Consider the following null and alternative hypotheses. Ho: P 0.16 Ha: P < 0.16 These hypotheses _______________. A. B. C. D. indicate a one-tailed test with a rejection area in the right tail indicate a one-tailed test with a rejection area in the left tail indicate a two-tailed test are established incorrectly 271 272 Test Bank C 31. E App B Consider the following null and alternative hypotheses. Ho: P = 0.16 Ha: P 0.16 These hypotheses _______________. A. B. C. D. 32. indicate a one-tailed test with a rejection area in the right tail indicate a one-tailed test with a rejection area in the left tail indicate a two-tailed test are established incorrectly Whenever hypotheses are established such that the alternative hypothesis is ">", then this would be a _______. E Term A. B. C. D. A Whenever hypotheses are established such that the alternative hypothesis is "not equal to", then this would be a _______ test. 33. two-tailed test one-tailed test Type II test Type I test E Term A. B. C. D. A If, in testing hypotheses, the researcher uses a method in which the probability of the calculated statistic is compared to alpha to reach a decision, the researcher is using the _______. 34. two-tailed one-tailed Type II Type I E Term A. B. C. D. A Suppose the alternative hypothesis in a hypothesis test is "the population mean is greater than 65". If the sample size is 50 and alpha =.05, the critical value of Z is _______. M Calc 35. A. B. C. D. probability method critical value method Z value method statistical method 1.645 -1.645 1.96 -1.96 Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations B 36. M Calc C M Calc D 38. E Calc C 39. M Calc A. 2.575 B. -2.575 C. 2.33 D. -2.33 In a two-tailed hypothesis about a population mean with a sample size of 100 and alpha = 0.10, the rejection region would be _______. Z>1.64 Z>1.28 Z<-1.28 and Z>1.28 Z<-1.64 and Z>1.64 In a two-tailed hypothesis about a population mean with a sample size of 100 and alpha = 0.05, the rejection region would be _______. A. B. C. D. 40. 1.645 -1.645 1.96 -1.96 Suppose the alternative hypothesis in a hypothesis test is "the population mean is greater than 60". If the sample size is 80 and alpha = .01, the critical value of Z is _______. A. B. C. D. E Calc C Suppose the alternative hypothesis in a hypothesis test is "the population mean is less than 60". If the sample size is 50 and alpha =.05, the critical value of Z is _______. A. B. C. D. 37. 273 Z>1.64 Z>1.96 Z<-1.96 and Z>1.96 Z<-1.64 and Z>1.64 Suppose you are testing the null hypothesis that a population mean is less than or equal to 80, against the alternative hypothesis that the population mean is greater than 80. If the sample size is 49 and alpha = .10, the critical value of Z is _______. A. B. C. D. 1.645 -1.645 1.28 -1.28 274 Test Bank A 41. M Calc A A. B. C. D. 42. M Calc A 43. M Calc 2 -2 14 -14 Suppose you are testing the null hypothesis that a population mean is greater than or equal to 60, against the alternative hypothesis that the population mean is less than 60. The sample size is 64 and =.05. If the sample mean is 58 and the sample standard deviation is 16, the calculated Z value is _______. A. B. C. D. 44. 1.645 -1.645 1.96 -1.96 Suppose you are testing the null hypothesis that a population mean is less than or equal to 80, against the alternative hypothesis that the population mean is greater than 80. The sample size is 49 and alpha =.05. If the sample mean is 84 and the sample standard deviation is 14, the calculated Z value is _______. A. B. C. D. M Calc C Suppose you are testing the null hypothesis that a population mean is less than or equal to 80, against the alternative hypothesis that the population mean is greater than 80. If the sample size is 49 and alpha =.05, the critical value of Z is _______. -1 1 -8 8 Suppose a researcher is testing a null hypothesis that = 61. A random sample of n = 36 is taken resulting in a sample mean of 63 and S=9. The calculated Z value is _______. A. B. C. D. -0.22 0.22 1.33 8 Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations B 45. M App B M App A 47. M App reject not reject redefine change the alternate hypothesis into A researcher is testing a hypothesis of a single mean. The critical Z value for =.05 and a two-tailed test is +1.96. The calculated Z value from sample data is 2.85. The decision made by the researcher based on this information is to _____ the null hypothesis. A. B. C. D. 48. reject not reject redefine change the alternate hypothesis into A researcher is testing a hypothesis of a single mean. The critical Z value for =.05 and a two-tailed test is +1.96. The calculated Z value from sample data is -1.85. The decision made by the researcher based on this information is to _____ the null hypothesis. A. B. C. D. M App A A researcher is testing a hypothesis of a single mean. The critical Z value for =.05 and a one-tailed test is 1.645. The calculated Z value from sample data is 1.13. The decision made by the researcher based on this information is to ______ the null hypothesis. A. B. C. D. 46. 275 reject not reject redefine change the alternate hypothesis into A researcher is testing a hypothesis of a single mean. The critical Z value for =.05 and a two-tailed test is +1.96. The calculated Z value from sample data is 2.11. The decision made by the researcher based on this information is to _____ the null hypothesis. A. B. C. D. reject not reject redefine change the alternate hypothesis into 276 Test Bank A 49. M App A A. B. C. D. 50. M App D A researcher is testing a hypothesis of a single mean. The critical Z value for = .01 and a one-tailed test is -2.33. The calculated Z value from sample data is -2.45. The decision made by the researcher based on this information is to _________ the null hypothesis. A researcher has a theory that the average age of managers in a particular industry is over 35-years-old, and he wishes to prove this. The null hypothesis to conduct a statistical test on this theory would be ____________. A. B. C. D. 51. reject not reject redefine change the alternate hypothesis into the population mean is < 35 the population mean is > 35 the population mean is = 35 the population mean is > 35 A company produces an item that is supposed to have a six inch hole punched in the center. A quality control inspector is concerned that the machine which punches the hole is "out-of-control" (hole is too large or too small). In an effort to test this, the inspector is going to gather a sample punched by the machine and measure the diameter of the hole. The alternative hypothesis used to statistical test to determine if the machine is out-of-control is M BApp A. B. C. D. D Jennifer Cantu, VP of Customer Services at Tri-State Auto Insurance, Inc., monitors the claims processing time of the claims division. Her standard includes "a mean processing time of 5 days or less." Each week, her staff checks for compliance by analyzing a random sample of 60 claims. Jennifer's null hypothesis is ________. 52. E BApp A. B. C. D. the mean diameter is > 6 inches the mean diameter is < 6 inches the mean diameter is = 6 inches the mean diameter is not equal to 6 inches >5 >5 n = 60 5 Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations A 53. E BApp C 54. 277 Jennifer Cantu, VP of Customer Services at Tri-State Auto Insurance, Inc., monitors the claims processing time of the claims division. Her standard includes "a mean processing time of 5 days or less." Each week, her staff checks for compliance by analyzing a random sample of 60 claims. Jennifer's alternative hypothesis is ________. A. > 5 B. 5 C. n = 60 D. 5 Jennifer Cantu, VP of Customer Services at Tri-State Auto Insurance, Inc., monitors the claims processing time of the claims division. Each week, her staff randomly selects a sample of 60 claims and tests the null hypothesis that the "mean processing time is 5 days or less." Jennifer chooses a 0.05 level of significance, the critical Z value is _____. E BCalc A. B. C. D. B Jennifer Cantu, VP of Customer Services at Tri-State Auto Insurance, Inc., monitors the claims processing time of the claims division. Each week, her staff randomly selects a sample of 60 claims and tests the null hypothesis that the "mean processing time is 5 days or less." Jennifer chooses a 0.01 level of significance, the critical Z value is _____. 55. E BCalc A. B. C. D. 1.96 -1.96 1.645 -1.645 -2.33 2.33 -2.58 2.58 278 Test Bank C 56. Jennifer Cantu, VP of Customer Services at Tri-State Auto Insurance, Inc., monitors the claims processing time of the claims division. Each week, her staff randomly selects a sample of 64 claims and tests the null hypothesis that the "mean processing time is 5 days or less" using a 0.10 level of significance. Last week the sample mean and standard deviation were 5.2 days and 0.56 days, respectively. The calculated Z value is _____. M BCalc A. B. C. D. D Jennifer Cantu, VP of Customer Services at Tri-State Auto Insurance, Inc., monitors the claims processing time of the claims division. Each week, her staff randomly selects a sample of 64 claims and tests the null hypothesis that the "mean processing time is 5 days or less" using a 0.05 level of significance. Last week the sample mean and standard deviation were 5.2 days and 0.56 days, respectively. The appropriate decision is _____. 57. 0.36 1.28 2.86 2.91 H BCalc A. B. C. D. C Jennifer Cantu, VP of Customer Services at Tri-State Auto Insurance, Inc., monitors the claims processing time of the claims division. Each week, her staff randomly selects a sample of 64 claims and tests the null hypothesis that the "mean processing time is 5 days or less" using a 0.05 level of significance. Last week the sample mean and standard deviation were 5.2 days and 1.56 days, respectively. The appropriate decision is _____. 58. H BCalc A. B. C. D. reduce the sample size increase the sample size do not reject the null hypothesis reject the null hypothesis reduce the sample size increase the sample size do not reject the null hypothesis reject the null hypothesis Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations A 59. 279 Restaurateur Denny Valentine is evaluating the feasibility of opening a restaurant in Richmond. The Chamber of Commerce estimates that "Richmond families, on the average, dine out at least 3 evenings per week." Denny plans to test this hypothesis using a random sample of 81 Richmond families. His null hypothesis is __________. 3 3 n = 81 <3 E BApp A. B. C. D. C Restaurateur Denny Valentine is evaluating the feasibility of opening a restaurant in Richmond. The Chamber of Commerce estimates that "Richmond families, on the average, dine out at least 3 evenings per week." Denny plans to test this hypothesis using a random sample of 81 Richmond families. His alternative hypothesis is __________. 60. 3 <3 <3 n = 81 E BApp A. B. C. D. A Restaurateur Denny Valentine is evaluating the feasibility of opening a restaurant in Richmond. The Chamber of Commerce estimates that "Richmond families, on the average, dine out at least 3 evenings per week." Denny plans to test this hypothesis at the 0.05 level of significance using a random sample of 81 Richmond families. The critical Z value is __________. 61. E BCalc A. B. C. D. -1.645 1.645 -1.96 1.96 280 Test Bank C 62. Restaurateur Denny Valentine is evaluating the feasibility of opening a restaurant in Richmond. The Chamber of Commerce estimates that "Richmond families, on the average, dine out at least 3 evenings per week." Denny plans to test this hypothesis at the 0.01 level of significance using a random sample of 81 Richmond families. The critical Z value is __________. E BCalc A. B. C. D. A Restaurateur Denny Valentine is evaluating the feasibility of opening a restaurant in Richmond. The Chamber of Commerce estimates that "Richmond families, on the average, dine out at least 3 evenings per week." Denny plans to test this hypothesis at the 0.01 level of significance. His random sample of 81 Richmond families produced a mean and a standard deviation of 2.7 and 0.9 evenings per week, respectively. The calculated Z value is __________. 63. -2.58 2.58 -2.33 2.33 M BCalc A. B. C. D. B Restaurateur Denny Valentine is evaluating the feasibility of opening a restaurant in Richmond. The Chamber of Commerce estimates that "Richmond families, on the average, dine out at least 3 evenings per week." Denny plans to test this hypothesis at the 0.01 level of significance. His random sample of 81 Richmond families produced a mean and a standard deviation of 2.7 and 0.9 evenings per week, respectively. The appropriate decision is __________. 64. H BCalc A. B. C. D. -3.00 3.00 -0.33 0.33 do not reject the null hypothesis reject the null hypothesis reduce the sample size increase the sample size Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations B 65. 281 Restaurateur Denny Valentine is evaluating the feasibility of opening a restaurant in Richmond. The Chamber of Commerce estimates that "Richmond families, on the average, dine out at least 3 evenings per week." Denny plans to test this hypothesis at the 0.01 level of significance. His random sample of 81 Richmond families produced a mean and a standard deviation of 2.7 and 1.8 evenings per week, respectively. The calculated Z value is __________. M BCalc A. B. C. D. A Restaurateur Denny Valentine is evaluating the feasibility of opening a restaurant in Richmond. The Chamber of Commerce estimates that "Richmond families, on the average, dine out at least 3 evenings per week." Denny plans to test this hypothesis at the 0.01 level of significance. His random sample of 81 Richmond families produced a mean and a standard deviation of 2.7 and 1.8 evenings per week, respectively. The appropriate decision is __________. 66. 1.50 -1.50 0.17 -0.17 H BCalc A. B. C. D. B Restaurateur Denny Valentine is evaluating the feasibility of opening a restaurant in Richmond. The Chamber of Commerce estimates that "Richmond families, on the average, dine out at least 3 evenings per week." Denny plans to test this hypothesis at the 0.01 level of significance. His random sample of 81 Richmond families produced a mean and a standard deviation of 2.5 and 1.8 evenings per week, respectively. The appropriate decision is __________. 67. H BCalc A. B. C. D. do not reject the null hypothesis reject the null hypothesis reduce the sample size increase the sample size do not reject the null hypothesis reject the null hypothesis reduce the sample size increase the sample size 282 Test Bank B 68. When the rod shearing process at Stockton Steel is "in control" it produces rods with a mean length of 120 inches. Periodically, quality control inspectors select a random sample of 36 rods. If the mean length of sampled rods is too long or too short, the shearing process is shut down. The null hypothesis is _________. E BApp A. B. C. D. C When the rod shearing process at Stockton Steel is "in control" it produces rods with a mean length of 120 inches. Periodically, quality control inspectors select a random sample of 36 rods. If the mean length of sampled rods is too long or too short, the shearing process is shut down. The alternative hypothesis is _________. 69. n = 36 = 120 120 n 36 E BApp A. B. C. D. D When the rod shearing process at Stockton Steel is "in control" it produces rods with a mean length of 120 inches. Periodically, quality control inspectors select a random sample of 36 rods. If the mean length of sampled rods is too long or too short, the shearing process is shut down. Sarah Shum, Director of Quality Programs, chose a 0.05 level of significance for this test. The critical Z values are _________. 70. E BCalc A. B. C. D. n = 36 = 120 120 n 36 -1.645 and 1.645 -1.75 and 1.75 -2.33 and 2.33 -1.96 and 1.96 Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations A 71. 283 When the rod shearing process at Stockton Steel is "in control" it produces rods with a mean length of 120 inches. Periodically, quality control inspectors select a random sample of 36 rods. If the mean length of sampled rods is too long or too short, the shearing process is shut down. Sarah Shum, Director of Quality Programs, chose a 0.10 level of significance for this test. The critical Z values are _________. E BCalc A. B. C. D. C When the rod shearing process at Stockton Steel is "in control" it produces rods with a mean length of 120 inches. Periodically, quality control inspectors select a random sample of 36 rods. If the mean length of sampled rods is too long or too short, the shearing process is shut down. The last sample showed a mean and standard deviation of 120.5 and 1.2 inches, respectively. Using = 0.05, the calculated Z value is _________. 72. -1.645 and 1.645 -1.75 and 1.75 -2.33 and 2.33 -1.96 and 1.96 M BCalc A. B. C. D. C When the rod shearing process at Stockton Steel is "in control" it produces rods with a mean length of 120 inches. Periodically, quality control inspectors select a random sample of 36 rods. If the mean length of sampled rods is too long or too short, the shearing process is shut down. The last sample showed a mean and standard deviation of 120.5 and 1.2 inches, respectively. Using = 0.05, the appropriate decision is _________. 73. H BCalc A. B. C. D. 0.42 -0.42 2.50 -2.50 do not reject the null hypothesis and shut down the process do not reject the null hypothesis and do not shut down the process reject the null hypothesis and shut down the process reject the null hypothesis and do not shut down the process 284 Test Bank B 74. When the rod shearing process at Stockton Steel is "in control" it produces rods with a mean length of 120 inches. Periodically, quality control inspectors select a random sample of 36 rods. If the mean length of sampled rods is too long or too short, the shearing process is shut down. The last sample showed a mean and standard deviation of 120.2 and 1.2 inches, respectively. Using = 0.05, the appropriate decision is _________. H BCalc A. B. C. D. B In performing a hypothesis test where the null hypothesis is that the population mean is 23 against the alternative hypothesis that the population mean is not equal to 23, a random sample of 17 items is selected. The sample mean is 24.6 and the sample standard deviation is 3.3. It can be assumed that the population is normally distributed. The degrees of freedom associated with this are _______. 75. E Calc B E Calc A. B. C. D. 76. do not reject the null hypothesis and shut down the process do not reject the null hypothesis and do not shut down the process reject the null hypothesis and shut down the process reject the null hypothesis and do not shut down the process 17 16 15 2 In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The degrees of freedom associated with this are _______. A. B. C. D. 25 24 26 2 Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations B 77. E Calc C E Calc C M Calc In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The level of significance is selected to be 0.10. The table "t" value for this problem is _______. A. B. C. D. 78. 1.318 1.711 2.492 2.797 In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The computed "t" value for this problem is _______. A. B. C. D. 79. 285 -12.5 12.5 -2.5 -0.7 In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9, a random sample of 16 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. The computed "t" value for this problem is _______. A. B. C. D. 0.05 0.20 0.33 1.33 286 Test Bank D 80. E Calc A A. B. C. D. 81. M Calc C In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9, a random sample of 16 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. The level of significance is selected as 0.05. The table "t" value for this problem is _______. In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9, a random sample of 16 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. The level of significance is selected as 0.05. The decision rule for this problem is to reject the null hypothesis if the computed "t" value is _______. A. B. C. D. 82. E BApp 1.753 2.947 2.120 2.131 less than -2.131 or greater than 2.131 less than -1.761 or greater than 1.761 less than -1.753 or greater than 1.753 less than -2.120 or greater than 2.120 The diameter of 3.5 inch diskettes is normally distributed. Periodically, quality control inspectors at Dallas Diskettes randomly select a sample of 16 diskettes. If the mean diameter of the diskettes is too large or too small the diskette punch is shut down for adjustment; otherwise, the punching process continues. The null hypothesis is _______. A. B. C. D. n 16 n = 16 = 3.5 3.5 Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations B 83. 287 The diameter of 3.5 inch diskettes is normally distributed. Periodically, quality control inspectors at Dallas Diskettes randomly select a sample of 16 diskettes. If the mean diameter of the diskettes is too large or too small the diskette punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.49 and 0.08 inches, respectively. Using = 0.05, the critical "t" values are _______. E BCalc A. B. C. D. D The diameter of 3.5 inch diskettes is normally distributed. Periodically, quality control inspectors at Dallas Diskettes randomly select a sample of 16 diskettes. If the mean diameter of the diskettes is too large or too small the diskette punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.49 and 0.08 inches, respectively. Using = 0.05, the appropriate decision is _______. 84. -2.120 and 2.120 -2.131 and 2.131 -1.753 and 1.753 -1.746 and 1.746 H BCalc A. B. C. D. A The diameter of 3.5 inch diskettes is normally distributed. Periodically, quality control inspectors at Dallas Diskettes randomly select a sample of 16 diskettes. If the mean diameter of the diskettes is too large or too small the diskette punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.55 and 0.08 inches, respectively. Using = 0.05, the appropriate decision is _______. 85. H BCalc A. B. C. D. reject the null hypothesis and shut down the punch reject the null hypothesis and do not shut down the punch do not reject the null hypothesis and shut down the punch do not reject the null hypothesis and do shut down the punch reject the null hypothesis and shut down the punch reject the null hypothesis and do not shut down the punch do not reject the null hypothesis and shut down the punch do not reject the null hypothesis and do not shut down the punch 288 Test Bank C 86. In performing hypothesis test about the population mean, the population standard deviation should be used if it is known. If it is not known, for large samples it can be approximated by _______. E Term A. B. C. D. A In performing hypothesis test about the population mean, the population standard deviation should be used if it is known. If it is not known, it can be approximated by the sample standard deviation if _______. 87. the sample mean the sample size the sample standard deviation the population variance M Term A. B. C. D. A A political scientist wants to prove that a candidate is currently carrying more than 60% of the vote in the state. She has her assistants randomly sample 200 eligible voters in the state by telephone and only 90 declare that they support her candidate. The calculated Z value for this problem is _______. 88. M Calc B A. B. C. D. 89. M BApp the sample size is at least thirty the sample is random the population mean is known the alpha is less than 0.10 -4.33 4.33 0.45 -.31 A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product are contacted. It is found that 50 of the 144 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the alternative hypothesis would be _______. A. B. C. D. the population proportion is less than 0.30 the population proportion is greater than 0.30 the population proportion is not equal to 0.30 the population mean is less than 40 Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations D 90. 289 A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product are contacted. It is found that 50 of the 144 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the calculated Z value would be _______. M BCalc A. B. C. D. A A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product are contacted. It is found that 50 of the 144 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the test would be _______. 91. 0.05 0.103 0.35 1.24 E BApp A. B. C. D. B Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standard's is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Ophelia's null hypothesis is _______. 92. E BApp A. B. C. D. a one-tailed test a two-tailed test an alpha test a finite population test P > 0.05 P 0.05 n = 30 n = 500 290 Test Bank C 93. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standard's is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using = 0.10, the critical Z value is _______. E BCalc A. B. C. D. A Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standard's is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using = 0.10, the calculated Z value is _______. 94. 1.645 -1.645 1.28 -1.28 M BCalc A. B. C. D. D Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standard's is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using = 0.10, the appropriate decision is _______. 95. H BCalc A. B. C. D. 1.03 -1.03 0.046 -0.046 reduce the sample size increase the sample size reject the null hypothesis do not reject the null hypothesis Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations C 96. 291 Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standard's is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 38 defaulted loans. Using = 0.10, the appropriate decision is _______. H BCalc A. B. C. D. C The executives of CareFree Insurance, Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Eighty employees rate the management as participatory. The null hypothesis is __________. 97. reduce the sample size increase the sample size reject the null hypothesis do not reject the null hypothesis E BApp A. B. C. D. A The executives of CareFree Insurance, Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Eighty employees rate the management as participatory. The critical Z value is __________. 98. E BCalc A. B. C. D. n = 30 n = 200 P 0.50 P < 0.50 -1.645 1.645 -1.96 1.96 292 Test Bank B 99. The executives of CareFree Insurance, Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Eighty employees rate the management as participatory. The appropriate decision is __________. H BCalc A. B. C. D. do not reject the null hypothesis reject the null hypothesis reduce the sample size increase the sample size A 100. The executives of CareFree Insurance, Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Ninety employees rate the management as participatory. The appropriate decision is __________. H BCalc A. B. C. D. D 101. Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of e-mail messages sent by GFS employees are not business related. A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were not business related. The null hypothesis is ____. E BApp A. B. C. D. A 102. Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of e-mail messages sent by GFS employees are not business related. A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were not business related. The critical Z value is ____. E BApp A. B. C. D. do not reject the null hypothesis reject the null hypothesis reduce the sample size increase the sample size = 30 n = 300 P < 0.25 P 0.25 -1.96 1.96 2.57 Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations 293 C 103. Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of e-mail messages sent by GFS employees are not business related. A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were not business related. The appropriate decision is _______. E BApp A. B. C. D. C 104. Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of e-mail messages sent by GFS employees are not business related. A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance. Sixty of the messages were not business related. The appropriate decision is _______. E BApp A. B. C. D. A 105. A two tailed hypothesis test about the mean is performed. The calculated Z value is 1.78. If alpha = 0.05, the correct decision would be _______. M Calc A. B. C. D. B 106. A two tailed hypothesis test about the mean is performed. The calculated Z value is 1.78. If alpha = 0.10, the correct decision would be _______. M Calc A. B. C. D. increase the sample size gather more data reject the null hypothesis do not reject the null hypothesis increase the sample size gather more data reject the null hypothesis do not reject the null hypothesis do not reject the null hypothesis reject the null hypothesis take a larger sample get a new calculator do not reject the null hypothesis reject the null hypothesis take a larger sample get a new calculator 294 Test Bank C 107. A null hypothesis was rejected at the 0.10 level of significance. It the level of significance were changed to 0.05 and the same sample results were obtained, what decision should be made? M App A. B. C. D. B 108. A null hypothesis was not rejected at the 0.10 level of significance. It the level of significance were changed to 0.05 and the same sample results were obtained, what decision should be made? M App A. B. C. D. B 109. What happens to the rejection region if the level of significance is changed from 0.10 to 0.05? E App A. B. C. D. A 110. What happens to the rejection region if the level of significance is changed from 0.05 to 0.10? E App A. B. C. D. D 111. A null hypothesis is P > 0.65. To test this hypothesis, a sample of 400 is taken and alpha is set at 0.05. If the true proportion is P = 0.60, what is the probability of a type II error? H Calc A. B. C. D. reject the null hypothesis do not reject the null hypothesis cannot be determined without further information all of the above reject the null hypothesis do not reject the null hypothesis cannot be determined without further information all of the above it gets larger it gets smaller it does not change all of the above it gets larger it gets smaller it does not change all of the above 0.17 0.45 0.95 0.67 Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations 295 D 112. Discrete Components, Inc. manufactures a line of electrical resistors. Presently, the carbon composition line is producing 100 ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically, the quality control inspectors check for conformity by randomly select 10 resistors from the line, and calculating the sample variance. The last sample had a variance of 4.36. Using = 0.05, the null hypothesis is _________________. E BApp A. B. C. D. B 113. Discrete Components, Inc. manufactures a line of electrical resistors. Presently, the carbon composition line is producing 100 ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically, the quality control inspectors check for conformity by randomly select 10 resistors from the line, and calculating the sample variance. The last sample had a variance of 4.36. Using = 0.05, the critical value of chi-square is _________________. E BCalc A. B. C. D. D 114. Discrete Components, Inc. manufactures a line of electrical resistors. Presently, the carbon composition line is producing 100 ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically, the quality control inspectors check for conformity by randomly select 10 resistors from the line, and calculating the sample variance. The last sample had a variance of 4.36. Using = 0.05, the calculated value of chi-square is _________________. E BCalc A. B. C. D. = 100 10 S2 4 2 4 18.31 16.92 3.94 3.33 1.74 1.94 10.90 9.81 296 Test Bank D 115. Discrete Components, Inc. manufactures a line of electrical resistors. Presently, the carbon composition line is producing 100 ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically, the quality control inspectors check for conformity by randomly select 10 resistors from the line, and calculating the sample variance. The last sample had a variance of 4.36. Using = 0.05, the appropriate decision is _________________. H BCalc A. B. C. D. B 116. David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. Based on a recent census of personnel, David knows that the variance of teller training time in the Southeast region is 8, and he wonders if the variance in the Southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the Southwest Region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Using = 0.10, the null hypothesis is ________. E BApp A. B. C. D. B 117. David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. Based on a recent census of personnel, David knows that the variance of teller training time in the Southeast region is 8, and he wonders if the variance in the Southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the Southwest Region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Using = 0.10, the critical values of chisquare are ________. M BCalc A. B. C. D. increase the sample size reduce the sample size reject the null hypothesis do not reject the null hypothesis = 25 2 = 8 2 = 4 2 8 7.96 and 26.30 6.57 and 23.68 -1.96 and 1.96 -1.645 and 1.645 Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations 297 A 118. David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. Based on a recent census of personnel, David knows that the variance of teller training time in the Southeast region is 8, and he wonders if the variance in the Southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the Southwest Region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Using = 0.10, the calculated value of chi-square is ________. E BCalc A. B. C. D. D 119. David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. Based on a recent census of personnel, David knows that the variance of teller training time in the Southeast region is 8, and he wonders if the variance in the Southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the Southwest Region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Using = 0.10, the appropriate decision is ________. H BCalc A. B. C. D. 28.00 30.00 56.00 60.00 increase the sample size reduce the sample size do not reject the null hypothesis reject the null hypothesis 298 Test Bank 120. M BApp The last operation on the 'dry line' at Canine Delights is a semiautomatic bag filling step. The dry line mixes, shapes, dries, and bags the five dry dog foods (one at a time) in Canine Delights' product line. Each of the five mixes is offered in 4 different sizes (5, 10, 15, and 25 pounds). When the bag filling machine is properly adjusted, the mean weight of the filled bags equals the advertised weight. Even so, the weight varies from bag to bag. Discuss statistical procedures for controlling the bag filling operation. Other than improper adjustment of the machine, what factors may account for the variability of the bags weights, or for an upward (downward) drift in the mean bag weight? What are the consequences of significantly overfilling (underfilling) the bags? _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations 121. M BApp 299 Carlos Cavazos, Director of Human Resources, is developing plans for an employee morale 'barometer.' First, he plans to measure the current morale level to use as a benchmark. Then, periodic (possibly monthly) measurements will be taken to track increases (decreases). His primary measuring instrument will be several 5-point scaled items (1 = totally depressed, 5 = it doesn't get any better than this). Carlos believes that, after the bugs are worked out, the system will allow management to assess the impact of managerial actions on employee morale. Describe the statistical methods which will be useful to Carlos, during the design and implementation of the morale barometer. What are the limitations of this system? What factors affect employee morale? _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ 300 Test Bank 122. Alan Lessoff, VP of Marketing at CyberWarehouse, Inc. (CWI), wants to know what makes a good web site for online shoppers. What design factors of a web site increase repeat visits by web shoppers? Color schemes? Graphics? Animations? Audio? Organization of pages? Ease of navigation? Opinion polls? E-mail feedback? Representatives of Web Shoppe Designs (WSD) claim that their team knows, and offer Alan a test trial of their design. Alan is inclined to accept the offer since it would be hosted, at no expense to CWI, on WSD's servers during the trial period. Alan has accumulated an extensive database of demographic data, and frequency of visits of repeat visitors to CWI web sites. The WSD representatives will collect comparable data during the trial period. Describe the statistical methods which will be useful to Alan at the conclusion of the trial period. M BApp Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations 123. 301 Online financial brokerages continue go grow with the Internet. CyberMarkets, Inc. (CMI) advises e-commerce businesses on their marketing strategies. Addalie McMinn, VP of Research at CMI, expects increasingly intense competition between online brokerages for new customers as the industry matures. She wants to learn more about the customers of online brokerages; she wants to understand "what makes them tick," so she can advise CMI clients how to compete more successfully. What factors do these investors use to choose one broker over another? Transaction costs? Basic service characteristics such as fast order execution, and timely, well-organized statements? Free tie-in services such as an address book, a calendar service, and links to favorite web sites for gifts. Should Addalie segment the customer population? Are all factors equally important for all market segments? Does age matter? Does gender matter? Does profession matter? Addalie has accumulated an extensive database of on traditional full-service brokerage customers. She plans to use summary measures from the database as benchmarks for comparisons with online customers. Describe the statistical methods that will be useful to Addalie during the study. M BApp 302 Test Bank