The branch manager of an outlet (Store 1) of a nationwide chain of pet supply stores wants to study characteristics of her customers. In particular, she decides to focus on two variables: the amount of money spent by customers and whether the customers own only one dog, only one cat, or more than one dog and/ or cat. The results from a sample of 70 customers are as follows:

• Amount of money spent: X-bar = $21.34, S = $9.22.

• Thirty- seven customers own only a dog.

• Twenty- six customers own only a cat.

• Seven customers own more than one dog and/ or cat.

a. Construct a 95% confidence interval estimate for the population mean amount spent in the pet supply store.

b. Construct a 90% confidence interval estimate for the population proportion of customers who own only a cat. The branch manager of another outlet (Store 2) wishes to conduct a similar survey in his store. The manager does not have access to the information generated by the manager of Store 1. 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 ± $1.50 if the standard deviation is estimated to be $ 10?

d. How many customers need to be selected to have 90% confidence of estimating the population proportion of customers who own only a cat to within ± 0.045?

e. Based on your answers to (c) and (d), how large a sample should the manager take?