MS1023 Business Statistics with Computer Applications Homework #4 MS1023 Business Statistics w/Comp Apps I Homework #4 - Use Red Par Score Form Chps. 9 & 10: 50 Questions Only 7. The rejection region for a hypothesis test becomes smaller if the level of significance is changed from 0.01 to 0.05. 1. The first step in testing a hypothesis is to establish a true null hypothesis and a false alternative hypothesis. a) True b) False a) True b) False 8. Whenever hypotheses are established such that the alternative hypothesis is ">8", where is the population mean, the hypothesis test would be a two-tailed test. 2. In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it. a) True b) False a) True b) False 3. The null and the alternative hypotheses must be mutually exclusive and collectively exhaustive. a) True b) False 4. Generally speaking, the hypotheses that business researchers want to prove are stated in the alternative hypothesis. a) True b) False 5. When a true null hypothesis is rejected, the researcher has made a Type I error. a) True b) False 6. When a false null hypothesis is rejected, the researcher has made a Type II error. a) True b) False Maho Sonmez maho.sonmez@utsa.edu 9. Whenever hypotheses are established such that the alternative hypothesis is " > 8", where is the population mean, the pvalue is the probability of observing a sample mean greater than the observed sample mean assuming that 8. a) True b) False 10. If a null hypothesis was not rejected at the 0.10 level of significance, it will be rejected at a 0.05 level of significance based on the same sample results. a) True b) False 11. Consider the following null and alternative hypotheses. Ho: 67 Ha: > 67 These hypotheses _______________. a) indicate a one-tailed test with a rejection area in the right tail b) indicate a one-tailed test with a rejection area in the left tail c) indicate a two-tailed test d) are established incorrectly e) are not mutually exclusive 1 MS1023 Business Statistics with Computer Applications Homework #4 12. Consider the following null and alternative hypotheses. Ho: p .16 Ha: p < .16 These hypotheses _______________. a) reject b) not reject c) redefine d) change the alternate hypothesis into e) restate a) indicate a one-tailed test with a rejection area in the right tail b) indicate a one-tailed test with a rejection area in the left tail c) indicate a two-tailed test d) are established incorrectly e) are not mutually exclusive 16. A researcher is testing a hypothesis of a single mean. The critical t value for = .05 and a two-tailed test is +2.0796. The observed t value from sample data is -2.92. The decision made by the researcher based on this information is to _____ the null hypothesis. 13. Suppose the alternative hypothesis in a hypothesis test is: "the population mean is less than 60". If the sample size is 27, is unknown, and alpha =.05, the critical value of t is _______. a) reject b) not reject c) redefine d) change the alternate hypothesis into e) restate a) 2.0555 b) -2.0555 c) -1.7056 d) -1.7033 e) -2.0518 17. 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 ______. 14. Suppose the alternative hypothesis in a hypothesis test is "the population mean is greater than 60". If the sample size is 24, is unknown, and alpha = .01, the critical value of t is _______. a) -2.8073 b) -2.7969 c) 2.8073 d) 2.4999 e) 2.4922 15. A researcher is testing a hypothesis of a single mean. The critical t value for = .05 and a one-tailed test is 2.0639. The observed t value from sample data is 1.742. The decision made by the researcher based on this information is to ______ the null hypothesis. Maho Sonmez maho.sonmez@utsa.edu a) n 16 b) n = 16 c) = 3.5 d) 3.5 e) 3.5 18. 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, 2 MS1023 Business Statistics with Computer Applications Homework #4 respectively. Using = 0.05, the appropriate decision is _______. 21. Using = 0.01, the appropriate decision is to _______ the null hypothesis. a) reject the null hypothesis and shut down the punch b) reject the null hypothesis and do not shut down the punch c) do not reject the null hypothesis and shut down the punch d) do not reject the null hypothesis and do not shut down the punch e) do nothing a) reject b) not reject c) redefine d) change the alternate hypothesis into e) restate The following data (in pounds), which were selected randomly from a normally distributed population of values, represent measurements of a machine part that is supposed to weigh, on average, 8.3 pounds. 8.1 8.4 8.2 8.5 8.4 8.3 8.3 8.7 8.3 8.4 8.1 8.2 8.2 8.3 8.5 8.8 8.4 8.6 8.2 8.5 Use these data and alpha = 0.01 to test the hypothesis that the parts average 8.3 pounds. Answer the questions 19-21 based on the above information. 19. The null hypothesis is ______. a) n 20 b) n = 20 c) = 8.3 d) 8.3 e) 8.3 Downtime in manufacturing is costly and can result in late deliveries, backlogs, failure to meet orders, and even loss of market share. Suppose a manufacturing plant has been averaging 23 minutes of downtime per day for the past several years, but during the past year, there has been a signicant effort by both management and production workers to reduce downtime. In an effort to determine if downtime has been signicantly reduced, company productivity researchers have randomly sampled 31 days over the past several months from company records and have recorded the daily downtimes shown below in minutes. Use these data and an alpha of .01 to test to determine if downtime has been signicantly reduced. Assume that daily downtimes are normally distributed in the population. 19 16 23 26 23 24 22 18 27 22 19 17 27 28 19 26 19 17 19 15 21 32 24 17 18 16 24 19 18 25 21 20. The critical value is ______. a) -2.8609 b) 2.8609 c) 2.8453 d) 2.5395 e) 2.8609 Maho Sonmez maho.sonmez@utsa.edu Answer the questions 22-25 based on the above information. 22. The alternative hypothesis is ______. a) = 23 3 MS1023 Business Statistics with Computer Applications b) > 23 c) 23 d) 23 e) < 23 23. The critical value is ______. a) -2.4528 b) 2.4528 c) 2.4573 d) -2.4573 e) 2.7500 24. Using = 0.01, the appropriate decision is to _______ the null hypothesis a) reject b) not reject c) redefine d) change the alternate hypothesis into e) restate 25. Using = 0.05, the appropriate decision is to _______ the null hypothesis a) reject b) not reject c) redefine d) change the alternate hypothesis into e) restate 26. 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 standards 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. The null hypothesis is _______. a) p 0.05 b) p 0.05 c) p > 0.05 Maho Sonmez maho.sonmez@utsa.edu Homework #4 d) p < 0.05 e) p = 0.05 27. 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 standards 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 _______. a) 1.645 b) -1.645 c) 1.28 d) -1.28 e) 2.28 28. 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 standards 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 observed z value is _______. a) 1.03 b) -1.03 c) 0.046 d) -0.046 e) 1.33 29. 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 standards 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 4 MS1023 Business Statistics with Computer Applications contained 30 defaulted loans. Using = 0.10, the appropriate decision is _______. a) reduce the sample size b) increase the sample size c) reject the null hypothesis d) do not reject the null hypothesis e) do nothing 30. 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 standards 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 _______. a) reduce the sample size b) increase the sample size c) reject the null hypothesis d) do not reject the null hypothesis e) do nothing 31. 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 __________. a) p 40 b) p < 40 c) p 0.50 d) p < 0.50 e) n > 200 32. A study by Hewitt Associates showed that 79% of companies offer employees exible scheduling. Suppose a researcher believes that in accounting rms this gure Maho Sonmez maho.sonmez@utsa.edu Homework #4 is lower. The researcher randomly selects 415 accounting rms and through interviews determines that 303 of these rms have exible scheduling. With a 1% level of signicance, does the test show enough evidence to conclude that a signicantly lower proportion of accounting rms offer employees exible scheduling? a) Reject the null hypothesis, concluding that the lower proportion of accounting firms offer employees flexible scheduling. b) Do not reject the null hypothesis, concluding that the lower proportion of accounting firms offer employees flexible scheduling. c) Reject the null hypothesis, concluding that the higher proportion of accounting firms offer employees flexible scheduling. d) Do not reject the null hypothesis, concluding that the higher proportion of accounting firms offer employees flexible scheduling. e) The test is inconclusive. Suppose a Realtor is interested in comparing the asking prices of midrange homes in Peoria, Illinois, and Evansville, Indiana. The Realtor conducts a small telephone survey in the two cities, asking the prices of midrange homes. A random sample of 21 listings in Peoria resulted in a sample average price of $116,900, with a standard deviation of $2,300. A random sample of 26 listings in Evansville resulted in a sample average price of $114,000, with a standard deviation of $1,750. The Realtor assumes prices of midrange homes are normally distributed and the variance in prices in the two cities is about the same. The researcher wishes to test whether there is any difference in the mean prices of midrange homes of the two cities for alpha = .01. 5 MS1023 Business Statistics with Computer Applications Answer the questions 33-36 based on the above information. 33. The null hypothesis for this problem is ______. a) 1 - 2 < 0 b) 1 - 2 > 0 c) 1 - 2 = 1 d) 1 - 2 0 e) 1 - 2 = 0 34. The degrees of freedom for this problem are _______. a) 20 b) 25 c) 46 d) 45 e) 43 35. The critical t value from table is ____. a) 2.6870 b) 2.6896 c) 2.4121 d) 2.0141 e) 1.6794 36. The appropriate decision for this problem is to _____________. Homework #4 nine car rental companies in Dallas results in a sample mean of $44 and a standard deviation of $3. Use alpha = 0.05 to test to determine whether the average daily car rental rates in Boston are signicantly higher than those in Dallas. Assume car rental rates are normally distributed and the population variances are equal. Answer the questions 37-40 based on the above information. 37. The null hypothesis for this problem is ______. a) 1 - 2 < 0 b) 1 - 2 > 0 c) 1 - 2 = 1 d) 1 - 2 0 e) 1 - 2 = 0 38. The degrees of freedom for this problem are _______. a) 7 b) 8 c) 9 d) 15 e) 16 a) not reject the null hypothesis, 1 - 2 = 0 b) reject the null hypothesis, 1 - 2 0 c) reject the null hypothesis 1 - 2 = 0 d) not reject the null hypothesis, 1 - 2 0 e) reject the null hypothesis 1 - 2 = 1 39. The critical t value from table is ____. Based on an indication that mean daily car rental rates may be higher for Boston than for Dallas, a survey of eight car rental companies in Boston is taken and the sample mean car rental rate is $47, with a standard deviation of $3. Further, suppose a survey of 40. The appropriate decision for this problem is to _____________. Maho Sonmez maho.sonmez@utsa.edu a) -1.7531 b) 1.7531 c) -2.1314 d) 2.1314 e) 1.6794 a) not reject the null hypothesis, 1 - 2 0 b) reject the null hypothesis, 1 - 2 0 c) reject the null hypothesis 1 - 2 = 0 6 MS1023 Business Statistics with Computer Applications d) reject the null hypothesis, 1 - 2 0 e) not reject the null hypothesis 1 - 2 0 41. A researcher wants to conduct a before/after study on 11 subjects to determine if a treatment results in any difference in scores. The null hypothesis is that the average difference is zero while the alternative hypothesis is that the average difference is not zero. Scores are obtained on the subjects both before and after the treatment. After subtracting the after scores from the before scores, the average difference is computed to be -2.40 with a sample standard deviation of 1.21. Assume that the differences are normally distributed in the population. The degrees of freedom for this test are _______. a) 11 b) 2 c) 9 d) 20 e) 10 42. A researcher wants to conduct a before/after study on 11 subjects to determine if a treatment results in any difference in scores. The null hypothesis is that the average difference is zero while the alternative hypothesis is that the average difference is not zero. Scores are obtained on the subjects both before and after the treatment. After subtracting the after scores from the before scores, the average difference is computed to be -2.40 with a sample standard deviation of 1.21. Assume that the differences are normally distributed in the population. The observed t value for this test is _______. a) -6.58 b) -21.82 c) -2.4 d) 1.98 e) 2.33 Maho Sonmez maho.sonmez@utsa.edu Homework #4 43. A researcher wants to conduct a before/after study on 11 subjects to determine if a treatment results in any difference in scores. The null hypothesis is that the average difference is zero while the alternative hypothesis is that the average difference is not zero. Scores are obtained on the subjects both before and after the treatment. After subtracting the after scores from the before scores, the average difference is computed to be -2.40 with a sample standard deviation of 1.21. A 0.05 level of significance is selected. Assume that the differences are normally distributed in the population. The table t value for this test is _______. a) 1.8125 b) 2.2622 c) 1.7959 d) 2.2281 e) 3.1693 One of the new thrusts of quality control management is to examine the process by which a product is produced. This approach also applies to paperwork. In industries where large long-term projects are undertaken, days and even weeks may elapse as a change order makes its way through a maze of approvals before receiving nal approval. This process can result in long delays and stretch schedules to the breaking point. Suppose a quality control consulting group claims that it can signicantly reduce the number of days required for such paperwork to receive approval. In an attempt to \"prove\" its case, the group selects ve jobs for which it revises the paperwork system. The following data show the number of days required for a change order to be approved before the group intervened and the number of days required for a change order to be approved 7 MS1023 Business Statistics with Computer Applications after the group instituted a new paperwork system. Before After 12 8 7 3 10 8 16 9 8 5 Use alpha = 0.05 to determine whether there was a significant drop in the number of days required to process paperwork to approve change orders. Assume that the differences in days are normally distributed. Homework #4 47. What is the appropriate critical value for this problem for alpha = 0.01? a) 4.6041 b) 4.0321 c) 3.3649 d) 4.5407 e) 3.7469 48. Mean sample difference ( ) is _______. a) 10.6 b) 6.6 c) 4 d) -4 e) 17.2 Answer the questions 44-50 based on the above information. 49. The observed value of t for this problem is __________. 44. The null hypothesis for this problem is _____. a) 4.78 b) 2.05 c) 4.87 d) -4.78 e) -2.05 a) D = 0 b) D 0 c) D 0 d) D 0 e) D 1 45. The degrees of freedom in this problem are _______. a) 3 b) 8 c) 5 d) 9 e) 4 50. The appropriate conclusion for this problem is ___________. a) not reject the null hypothesis, D 0 b) reject the null hypothesis, D 0 c) reject the null hypothesis D = 0 d) reject the null hypothesis, D 0 e) not reject the null hypothesis D 0 46. The sample standard deviation (sd) of the differences is _______. a) 1.6733 b) 1.6373 c) 1.8807 d) 1.8708 e) 1.8078 Maho Sonmez maho.sonmez@utsa.edu 8 41 E 42 A 43 B 44 a 45 e 46 d 47 a 48 c 49 a 50 c