412 Chapter 9 Hypothesis Testing Table 9.1 presents critical values for some commonly used significance levels ��. Table 9.1 Table of Critical Values Significance Level �� H1 0.10 0.05 0.02 0.01 Left-tailed −1.282 −1.645 −2.054 −2.326 Right-tailed 1.282 1.645 2.054 2.326 Two-tailed ±1.645 ±1.96 ±2.326 ±2.576 EXAMPLE 9.7 Find the critical region for a right-tailed alternate hypothesis A test is made of H0 : �� = 1 versus H1: �� > 1. The value of the test statistic is z = 1.85. a. Is H0 rejected at the �� = 0.05 level? b. Is H0 rejected at the �� = 0.01 level? Solution The alternate hypothesis is H1: �� > 1, so this is a right-tailed test. a. From Table 9.1, we see that the critical value for �� = 0.05 is z�� = 1.645. For a right-tailed test, we reject H0 if z ≥ z��. Because 1.85 > 1.645, we reject H0 at the �� = 0.05 level. b. The critical value for �� = 0.01 is 2.326. Because 1.85 < 2.326, we do not reject H0 at the �� = 0.01 level. Check Your Understanding 1. A test is made of H0 : �� = 25 versus H1: �� < 25. The value of the test statistic is z = −1.84. a. Find the critical value and the critical region for a significance level of �� = 0.05. −1.645, z ≤ −1.645 b. Do you reject H0 at the �� = 0.05 level? Yes c. Find the critical value and the critical region for a significance level of �� = 0.01. −2.326, z ≤ −2.326 d. Do you reject H0 at the �� = 0.01 level? No 2. A test is made of H0 : �� = 7.5 versus H1: �� > 7.5. The value of the test statistic is z = 2.71. a. Find the critical value and the critical region for a significance level of �� = 0.05. 1.645, z ≥ 1.645 b. Do you reject H0 at the �� = 0.05 level? Yes c. Find the critical value and the critical region for a significance level of �� = 0.01. 2.326, z ≥ 2.326 d. Do you reject H0 at the �� = 0.01 level? Yes 3. A test is made of H0 : �� = 12 versus H1: �� ≠ 12. The value of the test statistic is z = 1.78. a. Find the critical value and the critical region for a significance level of �� = 0.05. 1.96, −1.96, z ≤ −1.96 or z ≥ 1.96 b. Do you reject H0 at the �� = 0.05 level? No c. Find the critical value and the critical region for a significance level of �� = 0.01. 2.576, −2.576, z ≤ −2.576 or z ≥ 2.576 d. Do you reject H0 at the �� = 0.01 level? No Answers are on page 432.
navidi_monk_elementary_statistics_2e_ch7-9
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