Review Exercises (week 9: Confidence Intervals)

Review Exercises ( week 9: Confidence Intervals)

1. Waking times of 40 people who start work at 8:00 a.m. (in minutes past 5:00 a.m.)

Find (a) the point estimate of the population mean and

(b) the maximum error of estimate for a 90% confidence interval

In Exercises 2 and 3, construct the indicated confidence interval for the population mean, µ.

1. c = 0.95, , s = 0.277, n=100

1. c = 0.90, , s = 0.0013, n = 45

In Exercise 4 and 5, determine the minimum sufficient sample size.

1. Use the point estimate for σ from Exercise 1. Determine the minimum survey size that is necessary to be 95% confident that the sample mean length of work commute is within 10 minutes of the actual mean waking time.

1. Now, suppose you want 99% confidence with a maximum error of 2 minutes. How many people would it be necessary to survey?

In Exercises 5 and 6, find the critical value, , for the given confidence level c and sample size n.

5. c = 0.80, n = 8 6. c = 0.80, n = 22

In Exercises 7 and 8, find the maximum error of estimate for µ.

7. c = 0.90, s = 23.4, n = 16, 8. c = 0.95, s = 0.05, n = 25,

9. Construct the confidence interval for µ using the statistics in Exercise 7.

10. In a random sample of 15 CD players brought in for repair, the average repair cost was $80 and the standard deviation was $14. Construct a 90% confidence interval for µ. Assume the repair costs are normally distributed.

11. Repeat Exercise 10 using a 99% confidence interval.

In Exercise 12 and 13, let p be the proportion of the population who respond yes. Use the given information to find and .

12. In a survey of 850 college students, 357 balanced their checkbooks monthly.

13 In a survey of 209 Montana residents, 61 felt their financial status was worse than a year ago.

In Exercises 14 and 15, construct the indicated confidence interval for the population proportion p.

14. Use the sample in Exercise 12 with c = 0.95.

15. Use the sample in Exercise 13 with c = 0.90.

16. A study of Pennsylvania high school wrestlers found that 23% had sustained an injury while wrestling that year. Suppose you want to conduct a similar study on New York high school wrestlers, and you wish to estimate (with 95% confidence) the proportion of injured wrestlers within 5%.Use the prior study’s proportion to find the minimum required sample size.

In Exercises 17 and 18, construct the indicated values, and , needed to estimate for the given confidence level c and sample size n.

17. c = 0.95, n = 13 18. c = 0.99, n = 10

19 A random sample of the liquid content (in fluid ounces) of 16 beverage cans is shown.

14.816	14.863	14.814	14.998	14.965	14.824	14.884	14.838
14.916	15.021	14.974	14.856	14.860	14.772	14.980	14.919

Use a 95% level of confidence. Construct the indicated confidence interval for and . Assume the samples are each taken from a normally distributed population.

Дата добавления: 2015-11-04