6.2 EXERCISES BUILDING BASIC SKILLS AND VOCABULARY In Exercises 1-4, find the critical value to for the given confidence level c and sample size n. FOR EXTRA HELP 1. c = 0.90, n = 10 2. c = 0.95, n = 12 MyStatLab 3. c = 0.99, n = 16 4. c = 0.98. n = 20 In Exercises 5-8, find the margin of error for the given values of c, s, and n. 5. c = 0.95, s = 5, n = 16 6. c = 0.99, s = 3, n = 6 7. c = 0.90, s = 2.4, n = 12 8. c = 0.98, s = 4.7, n = 9 In Exercises 9-12, (a) construct the indicated confidence interval for the population mean u using a t-distribution. (b) If you had incorrectly used a normal distribution, which interval would be wider? 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 = 10 In Exercises 13-16, use the given confidence interval to find the margin of error and the sample mean. 13. (14.7, 22.1) 14. (6.17, 8.53) 15. (64.6, 83.6) 16. (16.2, 29.8) USING AND INTERPRETING CONCEPTS Constructing Confidence Intervals In Exercises 17 and 18, you are given the sample mean and the sample standard deviation. Assume the random variable is normally distributed and use a t-distribution to find the margin of error and construct a 95% confidence interval for the population mean. Interpret the results. If convenient, use technology to construct the confidence interval. 17. Commute Time to Work In a random sample of eight people, the mean commute time to work was 35.5 minutes and the sample standard deviation was 7.2 minutes. 18. Driving Distance to Work In a random sample of five people, the mean driving distance to work was 22.2 miles and the sample standard deviation was 5.8 miles. 19. You research commute times to work and find that the population standard deviation was 9.3 minutes. Repeat Exercise 17, using a normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results. 20. You research driving distances to work and find that the population standard deviation was 5.2 miles. Repeat Exercise 18, using a normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results