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 = $21.34, S = $9.22.
• 37 customers own only a dog.
• 26 customers own only a cat.
• 7 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?