7.3 EXERCISES SECTION 7.3 Hypothesis Testing for the Mean (s Unknown) 383 For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. Explain how to find critical values for a t@distribution. 2. Explain how to use a t@test to test a hypothesized mean m when s is unknown. What assumptions are necessary? In Exercises 3–8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance a and sample size n. 3. Left-tailed test, a = 0.10, n = 20 4. Left-tailed test, a = 0.01, n = 35 5. Right-tailed test, a = 0.05, n = 23 6. Right-tailed test, a = 0.01, n = 31 7. Two-tailed test, a = 0.05, n = 27 8. Two-tailed test, a = 0.10, n = 38 Graphical Analysis In Exercises 9–12, state whether each standardized test statistic t allows you to reject the null hypothesis. Explain. 9. (a) t = 2.091 10. (a) t = 1.4 (b) t = 0 (b) t = 1.42 (c) t = -2.096 (c) t = -1.402 t t0 = −2.086 1 2 3 4 −1 −3 −4 0 t t0 = 1.402 1 2 3 4 −1 −3 −2 −4 0 11. (a) t = -1.755 12. (a) t = -1.1 (b) t = -1.585 (b) t = 1.01 (c) t = 1.745 (c) t = 1.7 t −t0 = −1.725 t0 = 1.725 1 2 3 4 −1 −3 −2 −4 0 t −t0 = −1.071 t0 = 1.071 1 2 3 4 −1 −3 −2 −4 0 In Exercises 13–18, test the claim about the population mean m at the level of significance a. Assume the population is normally distributed. 13. Claim: m = 15; a = 0.01. Sample statistics: x = 13.9, s = 3.23, n = 36 14. Claim: m 7 25; a = 0.05. Sample statistics: x = 26.2, s = 2.32, n = 17 15. Claim: m Ú 8000; a = 0.01. Sample statistics: x = 7700, s = 450, n = 25 16. Claim: m … 1600; a = 0.02. Sample statistics: x = 1550, s = 165, n = 46 17. Claim: m 6 4915; a = 0.02. Sample statistics: x = 5017, s = 5613, n = 51 18. Claim: m≠52,200; a = 0.05. Sample statistics: x = 53,220, s = 2700, n = 34
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