My Notes Ask Teur How profitable are different sectors of the stock market? One

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My Notes Ask Teur 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 25 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 x114.4. A random sample of 39 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 10. Assume that .-3.2 and 2 3.3 (a) Categorize the problem below according to parameter being estimated, proportion p, mean , difference of means 1-12, or difference of proportions p1 -P2. Then solve the problem. O P1- p2 (b) Let 1 represent the population mean profit as a percentage of stockholder equity for retail stocks, and let u2 represent the population mean profit as a percentage of stockholder equity for utility stocks. Find a 99% confidence interval for 1-2-(Use 1 decimal place.) lower imit upper Imit (c) 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 99% 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? O Because the interval contains only positive numbers, we can say that the profit as a percentage of stockholder equity is higher for retail stocks. O Because the interval contains both positive and negative numbers, we can not say that the profit as a percentage of stockholder equity is higher for retail stocks. O We can not make any conclusions using this confidence interval O Because the interval contains only negative numbers, we can say that the profit as a percentage of stockholder equity is higher for utility stocks. Need Help? Red

Explanation / Answer

a)
mu1 - mu2

b)

x1 = 14.4 , s1 = 3.2 , n1 = 25
x2 = 10.1 , s2 = 3.3 , n2 = 39

z value at 99% = 2.578

CI = (x1 - x2) +/- z * sqrt(s1^2/n1 + s2^2/n2)
= ( 14.4 - 10.1) +/- 2.578 * sqrt(3.2^2/25 + 3.3^2/39)
= (2.1,6.5)
Lower limit = 2.1
Upper limit = 6.5

c)

Answer is Option A)

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