MS1023 Business Statistics w/Comp Apps I Homework #3B - Use Red Par Score Form Chps. 9 & 10: 100 Questions 1. A null hypothesis must always include the equality sign. a) True b) False 2. If the result of a hypothesis test is statistically significant, it must be considered a substantive result. a) True b) False 3. A hypothesis test always contains the possibility of committing one of two types of errors called Type I and Type II errors. a) True b) False 4. The null hypothesis is rejected if the p-value (i.e., the probability of getting a test statistic at least as extreme as the observed value) is greater than the significance level. a) True b) False 5. The first step in testing a hypothesis is to establish a true null hypothesis and a false alternative hypothesis. a) True b) False 6. 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 7. The null and the alternative hypotheses must be mutually exclusive and collectively exhaustive. a) True b) False 8. Generally speaking, the hypotheses that business researchers want to prove are stated in the alternative hypothesis. a) True b) False 9. When a true null hypothesis is rejected, the researcher has made a Type I error. a) True b) False 10. When a false null hypothesis is rejected, the researcher has made a Type II error. a) True b) False 11. The rejection region for a hypothesis test becomes smaller if the level of significance is changed from 0.01 to 0.05. a) True b) False 12. 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. a) True b) False 13. Whenever hypotheses are established such that the alternative hypothesis is " > 8", where is the population mean, the p-value is the probability of observing a sample mean greater than the observed sample mean assuming that 8. a) True b) False 14. 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 15. Hypotheses are ______________. a) statements of facts about business phenomena b) mathematical equations that describe business phenomena c) tentative explanations of business phenomena d) proofs of claims about business phenomena 16. All statistical hypotheses consist of two parts, __________ and __________. a) a null hypotheses; a full hypothesis b) a null hypothesis; a substitute hypothesis c) a null hypothesis; an alternative hypothesis d) a null hypothesis; a substantive hypothesis 17. The probability of committing a Type I error is called __________. a) the p-value b) the power of the test c) the strength of the test d) the level of significance 18. Which of the following is an example of a research hypothesis, i.e. a statement of what the researcher believes will be the outcome of an experiment or study? a) Companies with more than $1 billion in assets spend more than 10% of their annual budget on advertising. b) Washington, D.C., is the capital of the United States of America. c) An academic year is divided into semesters. d) An acre is equal to 4840 square yards. 19. In order to scientifically test the research hypotheses using sample data, it is necessary to set up a more formal hypothesis structure using __________. a) informal hypotheses b) statistical hypotheses c) substantive hypotheses d) scientific hypotheses 20. All statistical hypotheses consist of two parts, a null hypothesis and an alternate hypothesis. These two parts must be __________. a) mutually exclusive but not collectively exhaustive b) mutually exclusive and collectively exhaustive c) mutually exclusive and statistically independent d) collectively exhaustive and statistically independent 21. The null hypothesis in a hypothesis test contains a statement about the population parameter such as the population mean or population proportion. The decision to reject the null hypothesis will be made if the outcome of the study or the sample statistic such as sample mean or sample proportion is __________. a) very close to the hypothesized value of the population parameter b) equal to the hypothesized value of the population parameter c) somewhat close to the hypothesized value of the population parameter d) significantly different from the hypothesized value of the population parameter 22. In a hypothesis test, the test statistic computed from the sample data is considered extreme or significant if it is __________. a) very large b) very small c) highly unlikely to occur due to chance d) highly likely to occur due to chance 23. A statistically significant result __________. a) is never substantive b) is always substantive c) may or may not be substantive d) is substantive if it is highly significant 24. In hypothesis testing the statistical conclusion is either to reject or not to reject the null hypothesis based on the sample data. Which of the following statements is true? a) The conclusion is always free from error if the correct procedure is followed. b) The conclusion will never reject a true null hypothesis. c) The conclusion will always reject a false null hypothesis. d) The conclusion is always subject to error because it is based on sample data. 25. Generally speaking, new hypotheses that the business researchers want to \"prove\" are stated in the __________. a) null hypothesis b) alternate hypothesis c) sample statistic d) population parameter 26. If a company wants to prove that the proportion (p) of its revenues from overseas operations is more than 18%, the null and alternate hypotheses are __________. a) H0: p > 0.18 and H1: p < 0.18 b) H0: p = 0.18 and H1: p < 0.18 c) H0: p < 0.18 and H1: p > 0.18 d) H0: p 0.18 and H1: p > 0.18 27. A test of the hypotheses, H0: p 0.24 and H1: p > 0.24 is a __________. a) one-tailed test b) two-tailed test c) test of two sample means d) test of two sample proportions 28. A test of the hypotheses, H0: p = 0.32 and H1: p 0.32 is a __________. a) one-tailed test b) two-tailed test c) test of two sample means d) test of two sample proportions 29. A Type I error is committed when __________. a) the null hypothesis is true and it is not rejected b) the null hypothesis is true and it is rejected c) the null hypothesis is false and it is not rejected d) the null hypothesis is false and it is not rejected 30. A Type II error is committed when __________. a) the null hypothesis is true and it is not rejected b) the null hypothesis is true and it is rejected c) the null hypothesis is false and it is not rejected d) the null hypothesis is false and it is rejected 31. An analyst tested the null hypothesis 30 against the alternative hypothesis that < 30. The analyst reported a p-value of 0.07. For what significance level of will the null hypothesis would be rejected? a) > 0.07 b) = 0.07 c) 0.07 d) > 0.05 e) 0.05 < < 0.07 32. 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 33. Consider the following null and alternative hypotheses. Ho: p .16 Ha: p < .16 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 34. 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) 2.0555 b) -2.0555 c) -1.7056 d) -1.7033 e) -2.0518 35. 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) 2.4999 36. 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. a) reject b) not reject c) redefine d) change the alternate hypothesis into e) restate 37. 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. a) reject b) not reject c) redefine d) change the alternate hypothesis into e) restate 38. 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) n 16 b) n = 16 c) = 3.5 d) 3.5 e) 3.5 39. 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 _______. 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 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 8.1 8.4 8.3 8.3 8.4 8.2 8.5 8.5 8.5 8.6 8.7 8.4 8.3 8.4 8.2 8.8 8.2 Use these data and alpha = 0.01 to test the hypothesis that the parts average 8.3 pounds. Answer the questions 40-42 based on the above information. 40. The null hypothesis is ______. a) n 20 b) n = 20 c) = 8.3 d) 8.3 e) 8.3 8.2 8.3 41. The critical value is ______. a) -2.8609 b) 2.8609 c) 2.8453 d) 2.5395 e) 2.8609 42. 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 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 28 16 22 19 21 17 17 24 19 18 32 26 24 22 16 19 18 15 27 18 Answer the questions 43-46 based on the above information. 43. The alternative hypothesis is ______. a) = 23 b) > 23 c) 23 d) 23 e) < 23 44. The critical value is ______. a) -2.4528 b) 2.4528 c) 2.4573 d) -2.4573 e) 2.7500 17 25 24 23 19 19 23 26 27 21 45. 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 46. 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 47. The dean of a business school claims that the average starting salary of its graduates is more than 85 (in $000's). Sample data on the starting salaries of 64 randomly selected recent graduates yielded a mean of 88 (in $000s) and a sample standard deviation of 10 (in $000's). Which of the following sets of hypotheses is correct? a) H0: = 85 and Ha: 85 b) H0: = 85 and Ha: < 85 c) H0: 85 and Ha: > 85 d) H0: > 85 and Ha: < 85 e) H0: 85 and Ha: > 85 48. The dean of a business school claims that the average starting salary of its graduates is more than 85 (in $000's). Sample data on the starting salaries of 64 randomly selected recent graduates yielded a mean of 88 (in $000s) and a sample standard deviation of 10 (in $000's). What is the value of the sample test statistic? a) 2.00 b) 1.92 c) 1.30 d) 1.65 e) 2.40 49. The dean of a business school claims that the average starting salary of its graduates is more than 85 (in $000's). Sample data on the starting salaries of 64 randomly selected recent graduates yielded a mean of 88 (in $000s) and a sample standard deviation of 10 (in $000's). What is the critical value for the rejection region if the level of significance is 5%? a) 1.6690 b) -1.9977 c) 1.9983 d) 1.6694 e) -1.6694 50. The rejection region in a hypothesis test depends on __________. a) the power of test and the type of test (i.e., one-sided or two-sided) b) the significance level and the type of test (i.e., one-sided or two-sided) c) the power of the test and the significance level d) the sample size and the sample mean 51. If the calculated test statistic falls in the rejection region, the statistical action is to __________. a) reject the null hypothesis b) reject the alternate hypothesis c) reject both the hypotheses d) accept both the hypotheses 52. The probability of getting a test statistic as extreme as the observed test statistic computed from the sample data under the assumption that the null hypothesis is true is called the __________. a) critical value b) extreme value c) significance level d) p-value 53. When using the p-value to test hypotheses, the null hypothesis would be rejected if __________. a) the p-value is negative b) the p-value is greater than the significance level c) the p-value is greater than the power of the test (1 - ) d) the p-value is less than the significance level 54. In the testing of hypotheses about the population mean when the population is unknown, the critical values are determined using the __________. a) z-distribution b) t-distribution c) F- distribution d) -distribution 55. In the testing of hypotheses about the population mean, if the sample size is increased keeping other things like the significance level same, the critical mean values for the rejection region __________. a) remain the same b) move further away from the hypothesized value c) move closer to the hypothesized value d) change from z-distribution to t-distribution 56. In a one-sided test of the hypotheses about a population proportion, the p-value was found to be 0.045. The null hypothesis in this test would __________. a) be rejected if the significance level is = 0.05 b) not be rejected if the significance level is = 0.05 c) be rejected if the significance level is = 0.01 d) be rejected if the significance level is = 0.04 57. In the testing of hypotheses about the population proportion when the sample size is large enough to satisfy the central limit theorem the critical values are determined using the __________. a) binomial distribution b) t-distribution c) F- distribution d) z-distribution 58. To test if the means of two populations are different, we test the significance of the difference between two sample means. a)True b) False 59. To test if a training program has resulted in a significant difference in the average performance level of the workers, it is better to take two sets of independent samples: one from the group of workers who took the training and the other from the group of workers that did not take the training program. a)True b) False 60. To test if a training program has resulted in a significant difference in the average performance level of the workers a matched-pairs test must be used. a)True b) False 61. To determine if two brands of car tires differ in their performance measured in terms of the average wear over the first 10,000 miles, we should conduct __________. a) b) c) d) one hypothesis test for the difference in the two population means two hypotheses tests for population proportion for each brand two hypotheses tests for population mean one for each brand one hypothesis test for the difference in the two population proportions 62. To test the hypotheses about the difference in the means of two populations, we should use __________. a) b) c) d) the difference in the means of two populations the ratio in the means of two populations the ratio of the means of two samples the difference in the means of two samples 63. Independent random samples selected from two normal populations produced the sample means and standard deviations shown below: Sample 1 Sample 2 s1 = 3.46 n1 = 20 s2 = 5.2 n2 = 18 Conduct the test H0: 1 - 2 = 0 against Ha: 1 - 2 0, then the test statistic is __________. a) b) c) d) 1.97 -1.97 -1.93 1.93 64. If the populations are normally distributed and the population variances are unknown, the test statistic for testing the hypotheses about the difference between the two population means is based on the __________. a) t-distribution b) -distribution c) F-distribution d) z-distribution 65. If the populations are normally distributed and the population variances are equal but unknown, the t-statistic for testing the hypotheses about the difference between the two population means using samples of size 20 and 30 has a degree of freedom equal to ____. a) 50 b) 48 c) 29 d) 19 66. The computer output for a test of the hypotheses about the difference between the two population means using the t test showed a p-value of 0.0223. Which of the following statements is true? a) the null hypothesis is rejected at a significance level of 0.01 b) the null hypothesis is rejected at a significance level of 0.05 c) the null hypothesis is not rejected at a significance level of 0.05 d) the null hypothesis is rejected at a significance level of 0.001 67. To determine if a training program has improved the average performance of trainees data are collected on the performance of a sample of the trainees \"before\" and \"after\" the training. In this type of situations, the samples are __________. a) independent b) dependent c) uncorrelated d) unmatched 68. A human resources manager wants to conduct a \"before/after\" study on 16 employees to determine if a motivation seminar results in an increase in their ratings of the company. The afterratings are subtracted from the before-ratings to get the differences in the ratings and the average difference is computed to be -1.13 with a sample standard deviation of 2.4. The appropriate test statistic based on sample data for the test of the hypotheses is _____________. a) -1.683 b) -2.883 c) -1.983 d) -1.883 e) -1.083 69. A human resources manager wants to conduct a \"before/after\" study on 16 employees to determine if a motivation seminar results in an increase in their ratings of the company. The afterratings are subtracted from the before-ratings to get the differences in the ratings and the average difference is computed to be -1.13 with a sample standard deviation of 2.4. The critical or table value of the test statistic to set the decision rule in the test of the hypotheses at 0.05 level of significance is _____________. a) - 1.7613 b) - 1.7459 c) - 1.6973 d) - 2.1199 e) - 1.7531 70. To determine if a training program has improved the average performance of trainees if data is collected from two different groups of managers (one group that has not undertaken the training program and the other group that has completed the training program), the samples are __________. a) independent b) dependent c) correlated d) matched 71. To determine if a training program has improved the average performance of trainees the sample data must be based on __________. a) independent observations b) matched-pairs observations c) uncorrelated observations d) unmatched observation 72. In a hypothesis test to determine if a training program has improved the average performance of the trainees, data are collected from a sample of 30 trainees \"before\" and \"after\" the training. The tformula in this test has degrees of freedom equal to __________. a) 60 b) 59 c) 58 d) 29 73. A paired difference experiment produced the following results: Then for testing H0: D 0 against Ha: D > 0, the proper test statistic and the critical value of significance level 0.05 are __________. a) 5.73 and 1.6839 b) 5.66 and 1.6839 c) 5.73 and 2.0211 d) 5.66 and 2.0211 74. 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) -21.82 b) -6.58 c) -2.4 d) 1.98 e) 2.33 75. A researcher is conducting a matched-pairs study. She gathers data on each pair in the study resulting in: Pair Group 1 Group 2 1 10 12 2 8 9 3 11 11 4 8 10 5 9 12 Assume that the data are normally distributed in the population. The level of significance is selected to be 0.10. If the alternative hypothesis is that the average difference is greater than zero, the null hypothesis would be rejected if the observed value of t is _______. a) greater than 1.5332 b) less than -1.5332 c) greater than 2.1318 d) less than -2.1318 e) equal to 2.3534 76. 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 d) p < 0.05 e) p = 0.05 77. 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 78. 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 79. 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 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 80. 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 81. 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 82. A study by Hewitt Associates showed that 79% of companies offer employees exible scheduling. Suppose a researcher believes that in accounting rms this gure 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. Answer the questions 83-86 based on the above information. 83. 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 84. The degrees of freedom for this problem are _______. a) 20 b) 25 c) 46 d) 45 e) 43 85. The critical t value from table is ____. a) 2.6870 b) 2.6896 c) 2.4121 d) 2.0141 e) 1.6794 86. The appropriate decision for this problem is to _____________. 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 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 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 87-90 based on the above information. 87. 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 88. The degrees of freedom for this problem are _______. a) 7 b) 8 c) 9 d) 15 e) 16 89. The critical t value from table is ____. a) -1.7531 b) 1.7531 c) -2.1314 d) 2.1314 e) 1.6794 90. The appropriate decision for this problem is to _____________. 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) reject the null hypothesis, 1 - 2 0 e) not reject the null hypothesis 1 - 2 0 91. 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 92. 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 93. 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 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. Answer the questions 94-100 based on the above information. 94. The null hypothesis for this problem is _____. a) D = 0 b) D 0 c) D 0 d) D 0 e) D 1 95. The degrees of freedom in this problem are _______. a) 3 b) 8 c) 5 d) 9 e) 4 96. The sample standard deviation (sd) of the differences is _______. a) 1.6733 b) 1.6373 c) 1.8807 d) 1.8708 e) 1.8078 97. 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 98. Mean sample difference ( ) is _______. a) 10.6 b) 6.6 c) 4 d) -4 e) 17.2 99. The observed value of t for this problem is __________. a) 4.78 b) 2.05 c) 4.87 d) -4.78 e) -2.05 100. 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