a) Suppose an investment analyst takes a random sample of U.S equity mutual funds and calculates Sharp Ratio. The sample size is 100, and the average sharp ratio is 0.45. The sample has a standard deviation of 0.30. Calculate and interpret the 90 percent confidence interval for the population mean of all U.S. equity mutual funds by using a reliability factor based on the standard normal distribution.

b) A money manager wants to obtain a 95 percent confidence interval for fund inflows and outflows over the next six months for his existing clients. He begins by calling a random sample of 10 clients and inquiring about their planned additions to and withdrawals from the fund. The manager then computes the change in cash flow for each client sampled as a percentage change in total funds placed with the manager. A positive percentage indicates a net cash inflow to the clients account, and a negative percentage change indicates a net cash outflow from the clients account. The manager weights each response by the relative size of the account within the sample and then computes a weighted average. As a result of this process, the money manager computes a weighted average of 5.5 percent. Thus, a point estimate is that the total amount of funds under management will increase by 5.5 percent in the next six months. The standard deviation of the observations in the sample is 10

percent. A histogram of past data looks fairly close to normal, so the manager assumes the population is normal Calculate a 95 percent confidence interval for the population mean and interpret your findings. Using the sample mean of 5.5 percent and standard deviation of 10 percent, compute the confidence interval for sample sizes of 20 and 30. Interpret your results from Part a and Part b.