7.5 EXERCISES 400 CHAPTER 7 Hypothesis Testing with One Sample For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. Explain how to find critical values in a chi-square distribution. 2. Can a critical value for the chi-square test be negative? Explain. 3. How do the critical values for a two-tailed test change as a decreases? 4. Describe the difference between calculating the standardized test statistic, x 2, for a chi-square test for variance and a chi-square test for standard deviation. 5. How do the requirements for a chi-square test for a variance or standard deviation differ from a z@test or a t@test for a mean? 6. Explain how to test a population variance or a population standard deviation. In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance a. 7. Right-tailed test, 8. Right-tailed test, n = 27, a = 0.05 n = 10, a = 0.10 9. Left-tailed test, 10. Left-tailed test, n = 7, a = 0.01 n = 24, a = 0.05 11. Two-tailed test, 12. Two-tailed test, n = 81, a = 0.10 n = 61, a = 0.01 Graphical Analysis In Exercises 13 and 14, state whether each standardized test statistic x 2 allows you to reject the null hypothesis. Explain. 13. (a) x 2 = 2.091 14. (a) x 2 = 22.302 (b) x 2 = 0 (b) x 2 = 23.309 (c) x 2 = 6.3471 (c) x 2 = 8.457 2 4 6 8 10 2χ = 6.251 0 2χ 5 1015202530 2χ = 22.307 2χ = 8.547 R L 2χ In Exercises 15–22, test the claim about the population variance s 2 or standard deviation s at the level of significance a. Assume the population is normally distributed. 15. Claim: s 2 = 0.52; a = 0.05. Sample statistics: s 2 = 0.508, n = 18 16. Claim: s 2 = 63; a = 0.01. Sample statistics: s 2 = 58, n = 29 17. Claim: s 2 Ú 8.5; a = 0.05. Sample statistics: s 2 = 7.45, n = 23 18. Claim: s … 0.92; a = 0.01. Sample statistics: s = 0.67, n = 41 19. Claim: s 6 40; a = 0.01. Sample statistics: s = 40.8, n = 12 20. Claim: s 2 7 19; a = 0.1. Sample statistics: s 2 = 28, n = 17 21. Claim: s 2 ≠ 32.8; a = 0.1. Sample statistics: s 2 = 40.9, n = 101 22. Claim: s ≠ 24.9; a = 0.10. Sample statistics: s = 29.1, n = 51
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