14. Stocks: Retail and Utility How profitable are different sectors of the stock market? One way to answer such a question is to examine profit as a percentage of stockholder equity. A random sample of 32 retail stocks such as Toys “ R”

Us, Best Buy, and Gap was studied for x1, profit as a percentage of stockholder equity. The result was x1 5 13.7. A random sample of 34 utility (gas and electric)

stocks such as Boston Edison, Wisconsin Energy, and Texas Utilities was studied for x2, profit as a percentage of stockholder equity. The result was x2 5 10.1

(Source: Fortune 500, Vol. 135, No. 8). Assume that s1 5 4.1 and s2 5 2.7.

(a) Let m1 represent the population mean profit as a percentage of stockholder equity for retail stocks, and let m2 represent the population mean profit as a percentage of stockholder equity for utility stocks. Find a 95%

confidence interval for m1  m2.

(b) Interpretation Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 95% level of confidence, does it appear that the profit as a percentage of stockholder equity for retail stocks is higher than that for utility stocks?