61 The branch manager of an outlet (Store 1) of a nationwide chain of pet supply stores wants to study characteristics of her cus- tomers. In...

8.61 The branch manager of an outlet (Store 1) of a nationwide chain of pet supply stores wants to study characteristics of her cus- tomers. 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.
• Thirty-seven customers own only a dog.
• Twenty-six customers own only a cat.
• Seven customers own more than one dog and/or cat.

1. Construct a 95% confidence interval estimate for the popula- tion mean amount spent in the pet supply store.
2. Construct a 90% confidence interval estimate for the popula- tion 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% con- fidence 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? 

a ¿ ¿ the giveninformation :Sample mean ( X´ )=$ 21.34 nSample ¿(¿)=70Sample standard deviation ( s )=$ 9.22Here population standard deviation is unknown so we will use t−distribution...