6.2 EXERCISES SECTION 6.2 Confidence Intervals for the Mean (s Unknown) 315 For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. List six features that are common to both the standard normal curve and the t@distribution curve. 2. Describe how the t@distribution curve changes as the sample size increases. Finding Critical Values of t In Exercises 3–6, find the critical value tc for the level of confidence c and sample size n. 3. c = 0.90, n = 10 4. c = 0.95, n = 12 5. c = 0.99, n = 16 6. c = 0.98, n = 40 In Exercises 7 and 8, find the margin of error for the values of c, s, and n. 7. c = 0.95, s = 5, n = 16 8. c = 0.99, s = 3, n = 6 In Exercises 9–12, construct the indicated confidence interval for the population mean m using the t-distribution. Assume the population is normally distributed. 9. c = 0.90, x = 12.5, s = 2.0, n = 6 10. c = 0.95, x = 13.4, s = 0.85, n = 8 11. c = 0.98, x = 4.3, s = 0.34, n = 14 12. c = 0.99, x = 24.7, s = 4.6, n = 50 In Exercises 13 and 14, use the confidence interval to find the margin of error and the sample mean. 13. (14.7, 22.1) 14. (6.17, 8.53) In Exercises 15 and 16, find the t-value for the given values of x, m, s, and n. 15. x = 70.3, m = 64.8, s = 7.1, n = 16 16. x = 22.9, m=24.5, s = 4.3, n = 40 Using and Interpreting Concepts Constructing a Confidence Interval In Exercises 17–20, you are given the sample mean and the sample standard deviation. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 95% confidence interval for the population mean. Interpret the results. 17. Commute Time In a random sample of eight people, the mean commute time to work was 35.5 minutes and the standard deviation was 7.2 minutes. 18. Driving Distance In a random sample of five people, the mean driving distance to work was 22.2 miles and the standard deviation was 5.8 miles. 19. Cell Phone Prices In a random sample of eight cell phones, the mean full retail price was $526.50 and the standard deviation was $184.00. 20. Mobile Device Repair Costs In a random sample of 12 mobile devices, the mean repair cost was $90.42 and the standard deviation was $33.61. 21. You research commute times to work and find that the population standard deviation is 9.3 minutes. Repeat Exercise 17 using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.
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