The branch manager of a nationwide bookstore chain (located near a college campus) wants to study characteristics of her store's customers. She decides to focus on two variables: the amount of money spent by customers (on items other than textbooks) and whether the customers would consider purchasing educational DVDs related to graduate preparation exams, such as the GMAT, GRE, or LSAT. The results from a sample of 70 customers are as follows:
• Amount spent: = $28.52, S = $11.39.
• 28 customers stated that they would consider purchasing the educational DVDs.
a. Construct a 95% confidence interval estimate for the population mean amount spent in the bookstore.
b. Construct a 90% confidence interval estimate for the population proportion of customers who would consider purchasing educational DVDs. Assume that the branch manager of another store in the chain (also located close to a college campus) wants to conduct a similar survey in his store. Answer the following questions:
c. What sample size is needed to have 95% confidence of estimating the population mean amount spent in this store to within ± $2 if the standard deviation is assumed to be $10?
d. How many customers need to be selected to have 90% confidence of estimating the population proportion who would consider purchasing the educational DVDs to within ± 0.04?
e. Based on your answers to (c) and (d), how large a sample should the manager take?