6.4 EXERCISES 334 CHAPTER 6 Confidence Intervals For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. Does a population have to be normally distributed to use the chi-square distribution? 2. What happens to the shape of the chi-square distribution as the degrees of freedom increase? Finding Critical Values for x 2 In Exercises 3–8, find the critical values x 2 R and x 2 L for the level of confidence c and sample size n. 3. c = 0.90, n = 8 4. c = 0.99, n = 15 5. c = 0.95, n = 20 6. c = 0.98, n = 26 7. c = 0.99, n = 30 8. c = 0.80, n = 51 In Exercises 9–12, construct the indicated confidence intervals for (a) the population variance s 2 and (b) the population standard deviation s. Assume the sample is from a normally distributed population. 9. c = 0.95, s2 = 11.56, n = 30 10. c = 0.99, s2 = 0.64, n = 7 11. c = 0.90, s = 35, n = 18 12. c = 0.98, s = 278.1, n = 41 Using and Interpreting Concepts Constructing Confidence Intervals In Exercises 13–24, assume the sample is from a normally distributed population and construct the indicated confidence intervals for (a) the population variance s 2 and (b) the population standard deviation s. Interpret the results. 13. Bolts The diameters (in inches) of 18 randomly selected bolts produced by a machine are listed. Use a 95% level of confidence. 4.477 4.425 4.034 4.317 4.003 3.760 3.818 3.749 4.240 3.941 4.131 4.545 3.958 3.741 3.859 3.816 4.448 4.206 14. Drug Concentration The times (in minutes) for the drug concentration to peak when the drug epinephrine is injected into 15 randomly selected patients are listed. Use a 90% level of confidence. 4.87 9.67 3.43 8.19 2.92 12.56 19.08 8.70 10.02 9.89 8.37 11.18 6.78 15.55 8.88 15. Earnings The annual earnings (in thousands of dollars) of 21 randomly selected level 1 computer hardware engineers are listed. Use a 99% level of confidence. (Adapted from Salary.com) 59.4 85.2 86.5 80.2 67.4 79.8 70.8 52.4 69.5 75.4 79.9 65.0 68.8 79.1 61.3 85.4 78.1 72.6 95.5 67.6 76.2 16. Final Exam Scores The final exam scores of 24 randomly selected students in a statistics class are shown in the table at the left. Use a 95% level of confidence. 17. Space Shuttle Flights The durations (in days) of 14 randomly selected space shuttle flights have a sample standard deviation of 3.54 days. Use a 99% level of confidence. (Source: NASA) Final exam scores 61 73 59 99 83 60 68 69 97 43 61 87 55 40 67 48 87 64 55 90 59 71 65 59 TABLE FOR EXERCISE 16
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