Question: Suppose the Gap is considering putting a factory outlet store on Main Street and they hire you to conduct some required research. You implement a survey and ask 225 students how much they believe they would spend at the store each year. The student responses have a mean of $200 and a standard deviation of $150. Given this information, answer the following questions:

a. What is the 95% confidence interval for (true) mean per-student expenditure?

b. Form a lower bound for the (true) mean per-student expenditure. Use a 99% confidence interval.

c. Use a decision rule to test the hypothesis that the (true) mean per-student expenditure is less than $225. Use a 1% significance level.

d. Suppose you somehow knew that the true mean per-student expenditure was $215. What (approximately) is the probability that you would see a sample mean of $200 or lower if this was the case?