6.1 EXERCISES For Extra Help: MyLab Statistics SECTION 6.1 Confidence Intervals for the Mean (s Known) 305 Building Basic Skills and Vocabulary 1. When estimating a population mean, are you more likely to be correct when you use a point estimate or an interval estimate? Explain your reasoning. 2. Which statistic is the best unbiased estimator for m? (a) s (b) x (c) the median (d) the mode 3. For the same sample statistics, which level of confidence would produce the widest confidence interval? Explain your reasoning. (a) 90% (b) 95% (c) 98% (d) 99% 4. You construct a 95% confidence interval for a population mean using a random sample. The confidence interval is 24.9 6 m 6 31.5. Is the probability that m is in this interval 0.95? Explain. In Exercises 5–8, find the critical value zc necessary to construct a confidence interval at the level of confidence c. 5. c = 0.80 6. c = 0.85 7. c = 0.75 8. c = 0.97 Graphical Analysis In Exercises 9–12, use the values on the number line to find the sampling error. 9. 3.4 3.6 3.8 4.0 x 4.2 4.4 4.6 x = 3.8 = 4.27 μ 10. 8.6 8.8 9.0 9.2 x 9.4 9.6 9.8 x = 9.5 = 8.76 μ 11. 24 25 x 26 27 x = 26.43 = 24.67 μ 12. 46 47 x 48 49 μ x = 46.56 = 48.12 In Exercises 13–16, find the margin of error for the values of c, s, and n. 13. c = 0.95, s = 5.2, n = 30 14. c = 0.90, s = 2.9, n = 50 15. c = 0.80, s = 1.3, n = 75 16. c = 0.975, s = 4.6, n = 100 Matching In Exercises 17–20, match the level of confidence c with the appropriate confidence interval. Assume each confidence interval is constructed for the same sample statistics. 17. c = 0.88 18. c = 0.90 19. c = 0.95 20. c = 0.98 (a) x 54 55 56 57 58 59 60 57.2 54.9 59.5 (b) x 54 55 56 57 58 59 60 57.2 55.2 59.2 (c) x 54 55 56 57 58 59 60 57.2 55.6 58.8 (d) x 54 55 56 57 58 59 60 57.2 55.5 58.9 In Exercises 21–24, construct the indicated confidence interval for the population mean m. 21. c = 0.90, x = 12.3, s = 1.5, n = 50 22. c = 0.95, x = 31.39, s = 0.80, n = 82 23. c = 0.99, x = 10.50, s = 2.14, n = 45 24. c = 0.80, x = 20.6, s = 4.7, n = 100
RkJQdWJsaXNoZXIy NjM5ODQ=