For each hypothesis test in Problems 3-10, please provide the following information:
What is the level of significance? State the null and alternate hypotheses.
Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
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
Interpret your conclusion in the context of the application.
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 a confidence interval, thereby making the answer slightly more “conservative." Answers may vary due to rounding.
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 Us, Best Buy, and Gap was studied for x1, profit as a percentage of stockholder equity. The result was
Let
Examine the confidence interval and explain what it means in the context of this problem. Docs 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?
Test the claim that the profit as a percentage of stockholder equity for retail stocks is higher than that for utility stocks. Use
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Understanding Basic Statistics
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