Question: 4. You have collected data concerning SAT-Math scores from a sample of 27 Penn State statistics majors. Your sample has a mean of 720 and

4. You have collected data concerning SAT-Math scores from a sample of 27 Penn State statistics majors. Your sample has a mean of 720 and a standard deviation of 40. [20 points]

A. Construct a 95% confidence interval for the mean SAT-Math score of all Penn State statistics majors.

B. In the general population (i.e., students who are not statistics majors), the mean SAT-Math score is 500. Given your results from part (A), is there evidence that Penn State statistics majors are different from the general population in terms of their average SAT-Math score? Explain why.

C. If you wanted to construct a 95% confidence interval for SAT-Math score in all Penn State statistics majors with a margin of error of 10 points, what sample size would you need?

D. If you wanted to construct a 95% confidence interval for SAT-Math score in all Penn State statistics majors with a margin of error of 5 points, what sample size would you need?

E. Compare your results from part (C) and part (D). Which is larger? Explain why?

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