CHAPTER 9 CONFIDENCE INTERVAL ESTIMATION

31. You are trying to estimate the average amount a family spends on food during a year. In the past, the standard deviation of the amount a family has spent on food during a year has been approximately $1200. If you want to be 99% sure that you

have estimated average family food expenditures within $60, how many families do you need to survey?

32. You have been assigned to determine whether more people prefer Coke to Pepsi. Assume that roughly half the population prefers Coke and half prefers Pepsi. How large a sample would you need to take to ensure that you could estimate, with 95% confidence, the proportion of people preferring Coke within 3% of the actual value?

QUESTIONS 33 THROUGH 35 ARE BASED ON THE FOLLOWING INFORMATION:

A marketing research consultant hired by Coca-Cola is interested in determining the proportion of customers who favor Coke over other soft drinks. A random sample of 400 consumers was selected from the market under investigation and showed that 53% favored Coca-Cola over other brands.

33. Compute a 95% confidence interval for the true proportion of people who favor Coke. Do the results of this poll convince you that a majority of people favors Coke?

34. Suppose 2,000 (not 400) people were polled and 53% favored Coke. Would you now be convinced that a majority of people favor Coke? Why might your answer be different than in Question 33?

35. How many people would have to be surveyed to be 95% confident that you can estimate the fraction of people who favor Coca-Cola within 1%?

QUESTIONS 36 AND 37 ARE BASED ON THE FOLLOWING INFORMATION:

The employee benefits manager of a medium size business would like to estimate the proportion of full-time employees who prefer adopting plan A of three available health care plans in the coming annual enrollment period. A reliable frame of the company’s employees and their tentative health care preferences are available. Using Excel, the manager chose a random sample of size 50 from the frame. There were 17 employees in the sample who preferred plan A.

36. Construct a 99% confidence interval for the proportion of company employees who prefer plan A. Assume that the population consists of the preferences of all employees in the frame.

37. Interpret the 99% confidence interval constructed in Question 36.

QUESTIONS 38 THROUGH 40 ARE BASED ON THE FOLLOWING INFORMATION:

Q-Mart is interested in comparing its male and female customers. Q-Mart would like to know if its female charge customers spend more money, on average, than its male charge customers. They have collected random samples of 25 female customers and 22 male customers. On average, women charge customers spend $102.23 and men charge customers spend $86.46. Some information are shown below.

Summary statistics for two samples
	Female	Male
Sample sizes	25	22
Sample means	102.23	86.46
Sample standard deviations	93.393	59.695
Confidence interval for difference between means
Sample mean difference	15.77
Pooled standard deviation	79.466
Std error of difference	23.23

38. Using a t-value of 2.014, calculate a 95% confidence interval for the difference between the average female purchase and the average male purchase. Would you conclude that there is a significant difference between females and males in this case? Explain.

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39. What are the degrees of freedom for the t-statistic in this calculation? Explain how you would calculate the degrees of freedom in this case.

40. What is the assumption in this case that allows you to use the pooled standard deviation for this confidence interval?