1. How profitable are different sectors of the stock market? One way to answer such a question is to examine profit as a ercentage of stockholder equity. A random sample of32retail stocks such as Toys 'R' Us, Best Buy, and Gap was studied forx₁, profit as a percentage of stockholder equity. The result wasx₁=14.7.A random sample of33utility (gas and electric) stocks such as Boston Edison, Wisconsin Energy, and Texas Utilities was studied forx₂, profit as a percentage of stockholder equity. The result wasx₂=11.1.Assume that₁=3.1and₂=3.7.(a) Let₁represent the population mean profit as a percentage of stockholder equity for retail stocks, and let₂represent the population mean profit as a percentage of stockholder equity for utility stocks. Find a95% confidenceinterval for₁-₂.(Round your answers to two decimal places.)

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(b) 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? 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. (c) Test the claim that the profit as a percentage of stockholder equity for retail stocks is higher than that for utility stocks. Use= 0.01.(i) What is the level of significance? State the null and alternate hypotheses.H₀:₁=₂;H₁:₁>₂H₀:₁=₂;H₁:₁₂ H₀:₁<₂;H₁:₁=₂H₀:₁=₂;H₁:₁<₂ (ii) What sampling distribution will you use? What assumptions are you making?The Student'st. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations.The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? Compute the correspondingzortvalue as appropriate. (Test the difference₁₂.Round your answer to two decimal places.) (iii) Find (or estimate) theP-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to theP-value.

(iv) Based on your answers to parts (i)-(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level? At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (v) Interpret your conclusion in the context of the application. Fail to reject the null hypothesis, there is sufficient evidence to suggest that retail stocks have a higher percentage of stockholder equity when compared to utility stocks.Fail to reject the null hypothesis, there is insufficient evidence to suggest that retail stocks have a higher percentage of stockholder equity when compared to utility stocks. Reject the null hypothesis, there is insufficient evidence to suggest that retail stocks have a higher percentage of stockholder equity when compared to utility stocks.Reject the null hypothesis, there is sufficient evidence to suggest that retail stocks have a higher percentage of stockholder equity when compared to utility stocks.

2. A random sample of20adult male wolves from the Canadian Northwest Territories gave an average weightx₁=97lb with estimated sample standard deviations₁=6.3lb. Another sample of22adult male wolves from Alaska gave an average weightx₂=89lb with estimated sample standard deviations₂=7.1lb.(a) Let₁represent the population mean weight of adult male wolves from the Northwest Territories, and let₂represent the population mean weight of adult male wolves from Alaska. Find a 75% confidence interval for₁-₂. (Round your answers to one decimal place.)

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(b) 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 75% level of confidence, does it appear that the average weight of adult male wolves from the Northwest Territories is greater than that of the Alaska wolves?Because the interval contains only positive numbers, we can say that Canadian wolves weigh more than Alaskan wolves.Because the interval contains both positive and negative numbers, we can not say that Canadian wolves weigh more than Alaskan wolves. We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that Alaskan wolves weigh more than Canadian wolves. (c) Test the claim that the average weight of adult male wolves from the Northwest Territories is different from that of Alaska wolves. Use= 0.01.(i) What is the level of significance? State the null and alternate hypotheses. H₀:₁=₂;H₁:₁₂H₀:₁=₂;H₁:₁>₂ H₀:₁=₂;H₁:₁<₂H₀:₁₂;H₁:₁=₂ (ii) What sampling distribution will you use? What assumptions are you making? The Student'st. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations.The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? Compute the correspondingzortvalue as appropriate. (Test the difference₁₂.Round your answer to three decimal places.) (iii) Find (or estimate) theP-value. P-value > 0.2500.125 <P-value < 0.250 0.050 <P-value < 0.1250.025 <P-value < 0.0500.005 <P-value < 0.025P-value < 0.005 Sketch the sampling distribution and show the area corresponding to theP-value.

(iv) Based on your answers in parts (i)-(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level? At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. (v) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is insufficient evidence to suggest that the mean weights of the wolves are different in the two regions.Fail to reject the null hypothesis, there is sufficient evidence to suggest that the mean weights of the wolves are different in the two regions. Fail to reject the null hypothesis, there is insufficient evidence to suggest that the mean weights of the wolves are different in the two regions.Reject the null hypothesis, there is sufficient evidence to suggest that the mean weights of the wolves are different in the two regions.