# Confidence Interval & Sample Size

Difficult for me to comprehend! Several need to be answered with Excel.

1. If sample mean = 85, and n=64, construct a 95% confidence interval estimate for the population mean, mu.

2.The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. The manufacturer's specification that the the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and the sample mean amount of paint per 1-gallon can ins 0.995 gallon.

a. Construct a 99% confidence interval estimate for the population mean amount of paint included in a 1-gallon can.

b. On the basis of these results, do you think that the manager has a right to complain to the manufacturer? Why?

c. Must you assume that the population amount of paint per can is normally distributed here? Explain.

d. Construct a 95% confidence interval estimate. How does this change your answer in (b)?

3. If sample mean = 75, S = 24, and n = 36, and assuming that the population is normally distributed, construct a 95% confidence interval estimate for the population mean, mu.

4. The US Department of Transportation requires tire manufacturers to provide tire performance information on the sidewall of a tire to better inform prospective customers as they make purchasing decisions. One very important measure of tire performance is the tread wear index, which indicates the tire's resistance to tread wear compared with a tire graded with a base of 100. A tire with a a grade of 200 should last twice as long, on average, as a tire graded with a base of 100. A consumer organization wants to estimate the actual tread wear index of a brand name of tires that claims "graded 200" on the sidewall of the tire. A random sample of n=18 indicates a sample mean tread wear index of 195.3 and a sample standard deviation of 21.4.

a. Assuming that the population of tread wear indexes is normally distributed, construct a 95% confidence interval estimate for the population mean tread wear index for tires produced by this manufacturer under this brand name.

b.Do you think that the consumer organization should accuse the manufacturer of producing tires that do no meet the performance information provided on the sidewall of the tire? Explain.

c. Explain why an observed tread wear index of 210 for a particular tire is unusual, even though it is outside the confidence interval developed in (a).

5. The stocks included in the S&P 500 are those of large publicly held companies that trade on either the NY Stock Exchange or the NASDAQ. In 2008, the S&P 500 was down 38.5%, but what about financial compensation (salary,bonuses, stock option, etc.) to the 500 CEOs that run the companies? To learn more about hte mean CEO compensation, an alphabetical list of the 500 companies was obtained and oredered from 1 (3M) to 500 (Zions Bancorp). Next, the random number tables was used to select a random number from 1 to 50. The number selected was 10. Then the companies numbered 10, 60, 110, 160, 210, 260, 310, 360, 410, and 460 were investigated and the total CEO compensation recorded. The data, stored in CEO are as follows: see attachment.

a. Construct a 95% confidence interval estimate for the mean 2008 compensation for CEOs of S&P 500 companies.

b. Construct a 99% confidence interval estimate for the mean 2008 compensation for CEOs of S&P 500 companies.

c. Comment on the effect that changing the level of confidence had on your answers in (a) and (b).

6. CareerBuilder.com surveyed 1124 mothers who were currently employed full time. Of the women surveyed, 281 said that they were dissatisfied with their work-life balance, and 495 said that they would take a pay cut to spend more time with their kids.

a. Construct a 95% confidence interval estimate for the population proportion of mothers employed full time who are dissatisfied with their work-life balance.

b. Construct a 95% confidence interval estimate for the population proportion of mothers employed full time who would take a pay cut to spend more time with their kids.

c. Write a short summary of the information derived from (a) and (b).

7. In a survey of 1000 airline travelers, 760 responded that the airline fee that is most unreasonable is additional charges to redeem points/miles.

Construct a 95% confidence interval estimate for the population proportion of airline travelers who think that the airline fee that is mores unreasonable is additional charges to redeem points/miles.

8. If you want to bee 99% confident of estimating the population mean to within a sampling error of +/- 20 and the standard deviation is assumed to be 100, what sample size is required?

9. An advertising agency that serves a major radio station wants to estimate the mean amount of time that the station's audience spends listening to the radio daily. From past studies, the standard deviation is estimated as 45 minutes.

a. What sample size is needed if the agency wants to be 90% confident of being correct to within +/- 5 minutes?

b. If 99% confidence is desired, how many listeners need to be selected?

#### Solution Summary

Confidence Interval & Sample Size