Use the results of Problem 17 in Section 14.1 to answer the following questions:

(a) What is the mean rate of return for United Technologies stock if the rate of return of the S&P 500 is 4.2%?

(b) Construct a 90% confidence interval for the mean rate of return found in part (a).

(c) Predict the rate of return on United Technologies stock if the rate of return on the S&P 500 for a randomly selected month is 4.2%.

(d) Construct a 90% prediction interval for the rate of return found in part (c).

(e) Explain why the predicted rates of return found in parts (a) and (c) are the same, yet the intervals constructed in parts (b) and (d) are different.