A money manager wants to obtain a 90 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 change 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 -7.5 percent. Thus, a point estimate is that the total amount of funds under management will decrease by 7.5 percent in the next six months. The standard deviation of the observations in the sample is 25 percent. A histogram of past data looks close to normal, so the manager assumes the population is normal.

A. calculate a 90 percent confidence interval for the population mean and interpret your findings. The manager decides to see what the confidence interval would look like if he had used a sample size of 50 or 100 and found the same mean and standard deviation.

B. using the sample mean and standard deviation, compute the confidence interval for sample sizes of 50 and 100.

C. interpret your results from Parts A and B.