7.2 EXERCISES SECTION 7.2 Hypothesis Testing for the Mean (s Known) 373 For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. Explain the difference between the z@test for m using a P@value and the z@test for m using rejection region(s). 2. The mean of a random sample of 18 test scores is x = 85. The standard deviation of the population of all test scores is s = 6. Under what condition can you use a z@test to decide whether to reject a claim that the population mean is m = 88? Interpreting a P-Value In Exercises 3–8, the P@value for a hypothesis test is shown. Use the P@value to decide whether to reject H0 when the level of significance is (a) a = 0.01, (b) a = 0.05, and (c) a = 0.10. 3. P = 0.0461 4. P = 0.0691 5. P = 0.1271 6. P = 0.0107 7. P = 0.0838 8. P = 0.0062 Graphical Analysis In Exercises 9–12, match the P@value or z@statistic with the graph that represents the corresponding area. Explain your reasoning. 9. P = 0.0688 10. P = 0.2802 (a) z 1 2 3 −1 −2 −3 0 z = 1.08 (b) z 1 2 3 −1 −2 −3 0 z = 1.82 11. z = -2.37 12. z = -0.51 (a) z (b) z Finding a P-Value In Exercises 13–18, find the P@value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance a. 13. Left-tailed test 14. Left-tailed test z = -1.32 z = -1.55 a = 0.10 a = 0.05 15. Right-tailed test 16. Right-tailed test z = 2.46 z = 1.23 a = 0.01 a = 0.10 17. Two-tailed test 18. Two-tailed test z = -1.68 z = 1.95 a = 0.05 a = 0.08
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