C. Confidence Interval

1. Assume that the equity risk premium is normally distributed with a population mean of 6 percent and a population standard deviation of 18 percent. Over the last four years, equity returns (relative to the risk-free rate) have averaged 2.0 percent. You have a large client who is very upset and claims that results this poor should never occur. Evaluate your clients concerns.

A Construct a 95 percent confidence interval around the population mean for a sample of four-year returns.

B What is the probability of a 2.0 percent or lower average return over a four-year period?

2. Assume that monthly returns are normally distributed with a mean of 1 percent and a sample standard deviation of 4 percent. The population standard deviation is unknown. Construct a 95 percent confidence interval for the sample mean of monthly returns if the sample size is 24.