Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 19 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an employer averaged $10,646. The standard deviation of the sample was $994.
a. Based on this sample information, develop a 95 percent confidence interval for the population mean yearly premium.
b. How large a sample is needed to find the population mean within $233 at 99 percent confidence?