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 was studied for x1, profit as a percentage of stockholder equity. The result was x1 = 13.2. A random sample of 33 utility (gas and electric) stocks was studied for x2, profit as a percentage of stockholder equity. The result was x2 = 10.0. Assume ?1 = 4.2 and ?2 = 2.6. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some cases, this choice will increase the P-value by a small amount or increase the length of the confidence interval, thereby making the answer slightly more "conservative." (a) Let ?1 represent the population mean profit as a percentage of stockholder equity for retail stocks, and let ?2 represent the population mean profit as a percentage of stockholder equity for utility stocks. Find a 95% confidence interval for ?1 − ?2. (Round your answers to two decimal places.) lower limit upper limit (b) 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? What is the value of the sample test statistic? (Round your answer to two decimal places.) (iii) Find the P-value. (Round your answer to four decimal places.)
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 was studied for x1, profit as a percentage of stockholder equity. The result was
A random sample of 33 utility (gas and electric) stocks was studied for x2, profit as a percentage of stockholder equity. The result was
Assume ?1 = 4.2 and ?2 = 2.6. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some cases, this choice will increase the P-value by a small amount or increase the length of the confidence interval, thereby making the answer slightly more "conservative."
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(b) 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.
(iii) Find the P-value. (Round your answer to four decimal places.)
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