Section 6.1

1. When estimating a population parameter from sample statistics, rather than estimating a specific value, what is used?

2. If =12.74=12.74 and x=10.87x=10.87. What is the sampling error?

3. Let c=0.90c=0.90, =9.6=9.6, and n=34n=34. What is the margin of error, E?

Problems 4-5. Use the confidence interval for the population mean, (54.32,72.18)(54.32,72.18), to answer the questions.

4. What is the margin of error, EE?

5. What is the sample mean, xx?

6. Minimum sample size. Let c=0.95c=0.95, =10.4=10.4, and E=2.1E=2.1. What is the minimum sample size, nn, needed to estimate ? (see FAQ chapter 4.)

7. Repair Costs: Refrigerators. In a random sample of 50 refrigerators, the mean repair cost was $194.00. The population standard deviation, =$22.50=$22.50. Construct a 90% confidence interval for the population mean repair cost.

Section 6.2

Problems 8-10. Assume that is not known, the sample is random, and the population is normally distributed.

8. Let c=0.99c=0.99 and n=33n=33. Find the critical value, tctc.

9. Let c=0.95c=0.95, s=6.9s=6.9, and n=40n=40. Find the margin of error, EE.

10. Let c=0.98c=0.98, x=53.7x=53.7, s=6.4s=6.4, and n=32n=32. Construct a confidence interval for the population mean using the t-distribution.

Problems 11-12. Repair Costs: Computers. In a random sample of 20 computers, the mean repair cost was $142.40 and the standard deviation was $33.65. Assume the repair cost is normally distributed.

11. Use a t-distribution to construct a 99% confidence interval for the population mean .

12. What is the margin of error, EE?

Problems 13-15. Salaries. The monthly incomes for 14 randomly selected people, each with a bachelor's degree were gathered. Assume that the population of the monthly incomes is normally distributed. Use the data in Table 1 to answer the questions.

Salaries (Dollars)
6399.84	7072.61	5847.37	6746.40	7344.15	7091.05	6312.74
6107.86	7521.89	6540.86	7063.97	7045.74	7637.07	8049.48

13. What is the sample mean, xx?

14. What is the sample standard deviation, ss?

15. Construct a 90% confidence interval for the population mean .

Section 6.3

Problems 16-17. Let pp be the population proportion. In a survey of 5218 U.S. adults, 3642 say they have contributed to a charity in the past 12 months. Round results to 3 decimal places.

16. What is the point estimate, ^pp^, for pp?

17. What is the point estimate, ^qq^, for qq?

Problems 18-19. Let pp be the population proportion. In a survey of 2248 U.S. adults, 679 say they would go on vacation to Europe if cost did not matter. Round results to 3 decimal places.

1. What is the point estimate, ^pp^, for pp?
2. What is the point estimate, ^qq^, for qq?

Problems 20-22. In a survey of 5350 U.S. adults, 427 say they have traveled out of country in the past 12 months. Round your results to 3 decimal places.

20. Construct the 95% confidence interval for the population proportion pp.

21. Construct the 99% confidence interval for the population proportion pp.

22. Which of the two intervals you found is narrower? (Suggestion: plot the interval boundaries on a number line.)

Problems 23-25. Online Service Usage. You are a travel agent and wish to estimate, with 92% confidence, the proportion of vacationers who use an online service or the internet to make travel reservations. Your estimate must be accurate to within 5% of the population proportion. (Note: Do not use the c value for 90% or 95% to approximate the solution. Use the characteristics of c to find the best zczc value for a 92% level of confidence. See FAQ 4.11.)

23. Assume that no preliminary estimate is available. Find the minimum sample size needed.

24. Find the minimum sample size needed, using a prior study that found that 40% of the respondents said they used an online service or the internet to make travel reservations.

25. What do you conclude about the effects of having a preliminary estimate based on your results found in questions 23 and 24?