A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 95% confident that the sample mean is correct to within plus-or-minus $50 of the population mean. A previous study indicates that the standard deviation is approximately $400.
a) How large a sample size is needed?
b) If management wants to be correct to within plus-or-minus $25, what sample size is necessary?