Chapter 8, Problem 61PS

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 customer 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: $\bar{X}=\$21.34,S=\$\mathrm{9.22.}$

• Thirty-seven customers own only a dog.

• Twenty-six customer 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 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 this store. The manager does not have access to the information generated by the manager of Store 1. Answer the following questions:

a. What sample size is needed to have $95\%$ confidence of estimating the population mean spent in this store to within $\pm \$1.50$ if the standard deviation is estimated to be $\$10?$

b. How many customer need to be selected to have $90\%$ confidence of estimating the population proportion of customer who own only a cat to within $\pm 0.045?$

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