Question

Suppose that a random sample of 500 rates of return on mutual fund investment were computed and recorded. Assuming a standard deviation of all rates of return on mutual fund is 5.5% and sample mean is 15%.

(a) Estimate the mean rate of return on all mutual fund investments with 95% confidence. Interpret the estimate.

(b) Based on (a), the mutual fund agent claims that the mean return rate on mutual fund is 15%. Is that claim supported by the data?

Answer 1

A) At 95% confidence interval the critical value is z^* = 1.96

The 95% confidence interval for the population mean is

+/- z^* * /

= 15 +/- 1.96 * 5.5/

= 15 +/- 0.4821

= 14.5179, 15.4821

We are 95% confident that the true mean rate of return on all mutual fund investments will lie between the confidence limits 14.5179 and 15.4821.

B) Yes, the claim is supported by the data, because 15 lies in the confidence interval.