Section 9.2 Hypothesis Tests for a Population Mean, Standard Deviation Known 429 33. The P-value represents the probability that H0 is true. False 34. When presenting the results of a hypothesis test, one should report the P-value or the value of the test statistic. True Practicing the Skills 35. A test is made of H0 : �� = 50 versus H1: �� > 50. A sample of size n = 75 is drawn, and ̄x = 56. The population standard deviation is �� = 20. a. Compute the value of the test statistic z. 2.60 b. Is H0 rejected at the �� = 0.05 level? Yes c. Is H0 rejected at the �� = 0.01 level? Yes 36. A test is made of H0 : �� = 14 versus H1: �� ≠ 14. A sample of size n = 48 is drawn, and ̄x = 12. The population standard deviation is �� = 6. a. Compute the value of the test statistic z. −2.31 b. Is H0 rejected at the �� = 0.05 level? Yes c. Is H0 rejected at the �� = 0.01 level? No 37. A test is made of H0 : �� = 130 versus H1: �� ≠ 130. A sample of size n = 63 is drawn, and ̄x = 135. The population standard deviation is �� = 40. a. Compute the value of the test statistic z. 0.99 b. Is H0 rejected at the �� = 0.05 level? No c. Is H0 rejected at the �� = 0.01 level? No 38. A test is made of H0 : �� = 5 versus H1: �� < 5. A sample of size n = 87 is drawn, and ̄x = 4.5. The population standard deviation is �� = 25. a. Compute the value of the test statistic z. −0.19 b. Is H0 rejected at the �� = 0.05 level? No c. Is H0 rejected at the �� = 0.01 level? No 39. A test of the hypothesis H0 : �� = 65 versus H1: �� ≠ 65 was performed. The P-value was 0.035. Fill in the blank: If �� = 65, then the probability of observing a test statistic as extreme as or more extreme than the one actually observed is . 0.035 40. A test of the hypothesis H0 : �� = 150 versus H1: �� < 150 was performed. The P-value was 0.28. Fill in the blank: If �� = 150, then the probability of observing a test statistic as extreme as or more extreme than the one actually observed is . 0.28 41. True or false: If P = 0.02, then a. The result is statistically significant at the �� = 0.05 level. True b. The result is statistically significant at the �� = 0.01 level. False c. The null hypothesis is rejected at the �� = 0.05 level. True d. The null hypothesis is rejected at the �� = 0.01 level. False 42. True or false: If P = 0.08, then a. The result is statistically significant at the �� = 0.05 level. False b. The result is statistically significant at the �� = 0.10 level. True c. The null hypothesis is rejected at the �� = 0.05 level. False d. The null hypothesis is rejected at the �� = 0.10 level. True 43. A test of H0 : �� = 17 versus H1: �� < 17 is performed using a significance level of �� = 0.01. The value of the test statistic is z = −2.68. a. Is H0 rejected? Yes b. If the true value of �� is 17, is the result a Type I error, a Type II error, or a correct decision? Type I error c. If the true value of �� is 10, is the result a Type I error, a Type II error, or a correct decision? Correct decision 44. A test of H0 : �� = 50 versus H1: �� ≠ 50 is performed using a significance level of �� = 0.01. The value of the test statistic is z = 1.23. a. Is H0 rejected? No b. If the true value of �� is 50, is the result a Type I error, a Type II error, or a correct decision? Correct decision c. If the true value of �� is 65, is the result a Type I error, a Type II error, or a correct decision? Type II error 45. A test of H0 : �� = 0 versus H1: �� ≠ 0 is performed using a significance level of �� = 0.05. The P-value is 0.15. a. Is H0 rejected? No b. If the true value of �� is 1, is the result a Type I error, a Type II error, or a correct decision? Type II error c. If the true value of �� is 0, is the result a Type I error, a Type II error, or a correct decision? Correct decision 46. A test of H0 : �� = 6 versus H1: �� > 6 is performed using a significance level of �� = 0.01. The P-value is 0.002. a. Is H0 rejected? Yes b. If the true value of �� is 8, is the result a Type I error, a Type II error, or a correct decision? Correct decision c. If the true value of �� is 6, is the result a Type I error, a Type II error, or a correct decision? Type I error 47. If H0 is rejected at the �� = 0.05 level, which of the following is the best conclusion? iii i. H0 is also rejected at the �� = 0.01 level. ii. H0 is not rejected at the �� = 0.01 level. iii. We cannot determine whether H0 is rejected at the �� = 0.01 level. 48. If H0 is rejected at the �� = 0.01 level, which of the following is the best conclusion? i i. H0 is also rejected at the �� = 0.05 level. ii. H0 is not rejected at the �� = 0.05 level. iii. We cannot determine whether H0 is rejected at the �� = 0.05 level. 49. If P = 0.03, which of the following is the best conclusion? i i. If H0 is true, the probability of obtaining a test statistic as extreme as or more extreme than the one actually observed is 0.03. ii. The probability that H0 is true is 0.03. iii. The probability that H0 is false is 0.03. iv. If H0 is false, the probability of obtaining a test statistic as extreme as or more extreme than the one actually observed is 0.03. 50. If P = 0.25, which of the following is the best conclusion? iii i. The probability that H0 is true is 0.25. ii. If H0 is false, the probability of obtaining a test statistic as extreme as or more extreme than the one actually observed is 0.25. iii. If H0 is true, the probability of obtaining a test statistic as extreme as or more extreme than the one actually observed is 0.25. iv. The probability that H0 is false is 0.25.
navidi_monk_elementary_statistics_2e_ch7-9
To see the actual publication please follow the link above