Phone Solutions, Inc., specializes in providing call center services for companies that wish to outsource their call center activities. There are two main ways that Phone Solutions has historically billed its clients:

by the call or by the minute. Phone Solutions is currently negotiating with a new client who wants to be billed for the number of minutes that Phone Solutions is on the phone with customers. Before a contract is written, Phone Solutions plans to receive a random sample of calls and keep track of the minutes spent on the phone with the customer. From this it plans to estimate the mean call time. It wishes to develop a 95% confidence interval estimate for the population mean call time and wants this estimate to be within 0.15 minutes. The question is how many calls should Phone Solutions use in its sample?

Since the population standard deviation is unknown, a pilot sample was taken by having three call centers operated by Phone Solutions each take 50 calls for a total pilot sample of 150 calls. The minutes for each of these calls are listed in the file called PhoneSolutions.

a. How many additional calls will be needed to compute the desired confidence interval estimate for the population mean?

b. In the event that the managers at Phone Solutions want a smaller sample size, what options do they have? Discuss in general terms.