6 Review Exercises 338 CHAPTER 6 Confidence Intervals Section 6.1 1. The waking times (in minutes past 5:00 a.m.) of 40 people who start work at 8:00 a.m. are shown in the table at the left. Assume the population standard deviation is 45 minutes. Find (a) the point estimate of the population mean m and (b) the margin of error for a 90% confidence interval. 2. The driving distances (in miles) to work of 30 people are shown in the table at the left. Assume the population standard deviation is 8 miles. Find (a) the point estimate of the population mean m and (b) the margin of error for a 95% confidence interval. 3. (a) Construct a 90% confidence interval for the population mean in Exercise 1. Interpret the results. (b) Does it seem likely that the population mean could be within 10% of the sample mean? Explain. 4. (a) Construct a 95% confidence interval for the population mean in Exercise 2. Interpret the results. (b) Does it seem likely that the population mean could be greater than 12.5 miles? Explain. In Exercises 5 and 6, use the confidence interval to find the margin of error and the sample mean. 5. (20.75, 24.10) 6. (7.428, 7.562) 7. Determine the minimum sample size required to be 95% confident that the sample mean waking time is within 10 minutes of the population mean waking time. Use the population standard deviation from Exercise 1. 8. Determine the minimum sample size required to be 99% confident that the sample mean driving distance to work is within 2 miles of the population mean driving distance to work. Use the population standard deviation from Exercise 2. Section 6.2 In Exercises 9 –12, find the critical value tc for the level of confidence c and sample size n. 9. c = 0.80, n = 10 10. c = 0.95, n = 24 11. c = 0.98, n = 15 12. c = 0.99, n = 30 In Exercises 13–16, (a) find the margin of error for the values of c, s, and n, and (b) construct the confidence interval for m using the t-distribution. Assume the population is normally distributed. 13. c = 0.90, s = 25.6, n = 16, x = 72.1 14. c = 0.95, s = 1.1, n = 25, x = 3.5 15. c = 0.98, s = 0.9, n = 12, x = 6.8 16. c = 0.99, s = 16.5, n = 20, x = 25.2 17. In a random sample of 36 top-rated roller coasters, the average height is 165 feet and the standard deviation is 67 feet. Construct a 90% confidence interval for m. Interpret the results. (Source: POP World Media, LLC) 18. You research the heights of top-rated roller coasters and find that the population mean is 160 feet. In Exercise 17, does the t-value fall between -t0.95 and t0.95? Waking times (in minutes past 5:00 A.M.) 135 145 95 140 135 95 110 50 90 165 110 125 80 125 130 110 25 75 65 100 60 125 115 135 95 90 140 40 75 50 130 85 100 160 135 45 135 115 75 130 TABLE FOR EXERCISE 1 Driving distances to work (in miles) 12 9 7 2 8 7 3 27 21 10 13 7 2 30 7 6 13 6 4 1 10 3 13 6 2 9 2 12 16 18 TABLE FOR EXERCISE 2
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