364 CHAPTER 7 Hypothesis Testing with One Sample Left-Tailed Test z 1 2 3 −1 −2 −3 0 z = −2.23 The area to the left of z = −2.23 is P = 0.0129. Two-Tailed Test z 1 2 3 −1 −2 −3 0 z = 2.14 The area to the right of z = 2.14 is 0.0162, so P = 2(0.0162) = 0.0324. Finding a P-Value for a Left-Tailed Test Find the P@value for a left-tailed hypothesis test with a standardized test statistic of z = -2.23. Decide whether to reject H0 when the level of significance is a = 0.01. SOLUTION The figure at the left shows the standard normal curve with a shaded area to the left of z = -2.23. For a left-tailed test, P = 1Area in left tail2. Using Table 4 in Appendix B, the area corresponding to z = -2.23 is 0.0129, which is the area in the left tail. So, the P@value for a left-tailed hypothesis test with a standardized test statistic of z = -2.23 is P = 0.0129. You can check your answer using technology, as shown below. EXCEL =NORM.DIST(-2.23,0,1,TRUE) 0.012873721 A 1 Interpretation Because the P@value of 0.0129 is greater than 0.01, you fail to reject H0. TRY IT YOURSELF 2 Find the P@value for a left-tailed hypothesis test with a standardized test statistic of z = -1.71. Decide whether to reject H0 when the level of significance is a = 0.05. Answer: Page A40 Finding a P-Value for a Two-Tailed Test Find the P@value for a two-tailed hypothesis test with a standardized test statistic of z = 2.14. Decide whether to reject H0 when the level of significance is a = 0.05. SOLUTION The figure at the left shows the standard normal curve with shaded areas to the left of z = -2.14 and to the right of z = 2.14. For a two-tailed test, P = 21Area in tail of standardized test statistic2. Using Table 4, the area corresponding to z = 2.14 is 0.9838. The area in the right tail is 1 - 0.9838 = 0.0162. So, the P@value for a two-tailed hypothesis test with a standardized test statistic of z = 2.14 is P = 210.01622 = 0.0324. Interpretation Because the P@value of 0.0324 is less than 0.05, you reject H0. TRY IT YOURSELF 3 Find the P@value for a two-tailed hypothesis test with a standardized test statistic of z = 1.64. Decide whether to reject H0 when the level of significance is a = 0.10. Answer: Page A40 EXAMPLE 2 EXAMPLE 3
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