Question: Last year, consumers increasingly bought fleece (industry jargon for hotselling jogging suits, which now rival jeans as the uniform for casual attire). A New York designer of jogging suits is interested in the new trend and wants to estimate the amount spent per person on jogging suits during the year. The designer knows that people who belong to health and fitness clubs will have different buying behavior than people who do not. Furthermore, the designer finds that, within the proposed study area, 18% of the population are members of health and fitness clubs. A random sample of 300 people is selected, and the sample is proportionally allocated to the two strata: members of health clubs and nonmembers of health clubs. It is found that among members, the average amount spent is $152.43 and the standard deviation is $25.77, while among the nonmembers, the average amount spent is $15.33 and the standard deviation is $5.11.
a. What is the stratified estimate of the mean?
b. What is the standard error of the estimator?
c. Give a 90% confidence interval for the population mean µ.
d. Discuss one possible problem with the data.