418 Chapter 9 Hypothesis Testing SUMMARY To make a decision whether to reject H0 when using the P-value method: ∙ Choose a significance level �� between 0 and 1. ∙ Compute the P-value. ∙ If P ≤ ��, reject H0. If P > ��, do not reject H0. If P ≤ ��, we say that H0 is rejected at the �� level, or that the result is statistically significant at the �� level. EXAMPLE 9.12 Find the P-value In Example 9.9, the P-value was P = 0.0122. a. Do you reject H0 at the �� = 0.05 level? b. Do you reject H0 at the �� = 0.01 level? c. Is the result statistically significant at the �� = 0.05 level? d. Is the result statistically significant at the �� = 0.01 level? Solution a. Because P ≤ 0.05, we reject H0 at the �� = 0.05 level. b. Because P > 0.01, we do not reject H0 at the �� = 0.01 level. c. We reject H0 at the �� = 0.05 level, so the result is statistically significant at the �� = 0.05 level. d. We do not reject H0 at the �� = 0.01 level, so the result is not statistically significant at the �� = 0.01 level. Check Your Understanding 11. A hypothesis test is performed with a significance level of �� = 0.05. a. If the P-value is 0.08, is H0 rejected? No b. If the P-value is 0.08, are the results statistically significant at the 0.05 level? No c. If the P-value is 0.03, is H0 rejected? Yes d. If the P-value is 0.03, are the results statistically significant at the 0.05 level? Yes 12. For each of the following P-values, state whether H0 will be rejected at the 0.10 level. a. P = 0.12 No b. P = 0.07 Yes c. P = 0.05 Yes d. P = 0.20 No 13. For each of the following P-values, state whether the result is statistically significant at the 0.10 level. a. P = 0.08 Yes b. P = 0.15 No c. P = 0.01 Yes d. P = 0.50 No Answers are on page 433. The assumptions for using the P-value method are the same as for the critical value method. We repeat these assumptions here. Assumptions for Performing a Hypothesis Test About �� When �� Is Known 1. We have a simple random sample. 2. The sample size is large (n > 30), or the population is approximately normal.
navidi_monk_elementary_statistics_2e_ch7-9
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