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 27 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 = 14.4. A random sample of 36 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 = 9.7. Assume that σ1 = 3.1 and σ2 = 2.9. (a) Categorize the problem below according to parameter being estimated, proportion p, mean μ, difference of means μ1 – μ2, or difference of proportions p1 – p2. Then solve the problem. pμ p1 – p2μ1 – μ2 (b) Let μ1 represent the population mean profit as a percentage of stockholder equity for retail stocks, and let μ2 represent the population mean profit as a percentage of stockholder equity for utility stocks. Find a 90% confidence interval for μ1 – μ2. (Use 1 decimal place.) lower limit upper limit (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 90% 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? Because the interval contains only positive numbers, we can say that the profit as a percentage of stockholder equity is higher for retail stocks.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. We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that the profit as a percentage of stockholder equity is higher for utility stocks.

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 27 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 = 14.4. A random sample of 36 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 = 9.7. Assume that σ1 = 3.1 and σ2 = 2.9. (a) Categorize the problem below according to parameter being estimated, proportion p, mean μ, difference of means μ1 – μ2, or difference of proportions p1 – p2. Then solve the problem. pμ p1 – p2μ1 – μ2 (b) Let μ1 represent the population mean profit as a percentage of stockholder equity for retail stocks, and let μ2 represent the population mean profit as a percentage of stockholder equity for utility stocks. Find a 90% confidence interval for μ1 – μ2. (Use 1 decimal place.) lower limit upper limit (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 90% 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? Because the interval contains only positive numbers, we can say that the profit as a percentage of stockholder equity is higher for retail stocks.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. We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that the profit as a percentage of stockholder equity is higher for utility stocks.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.3: Modeling Data With Power Functions

Problem 6E: Urban Travel Times Population of cities and driving times are related, as shown in the accompanying...

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(a) Categorize the problem below according to parameter being estimated, proportion p, mean μ, difference of means μ₁ – μ₂, or difference of proportions p₁ – p₂. Then solve the problem.

pμ p₁ – p₂μ₁ – μ₂

(b) Let μ₁ represent the population mean profit as a percentage of stockholder equity for retail stocks, and let μ₂ represent the population mean profit as a percentage of stockholder equity for utility stocks. Find a 90% confidence interval for μ₁ – μ₂. (Use 1 decimal place.)

lower limit
upper limit

(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 90% 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?

Because the interval contains only positive numbers, we can say that the profit as a percentage of stockholder equity is higher for retail stocks.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. We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that the profit as a percentage of stockholder equity is higher for utility stocks.

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