Question: 3. A random sample of 1000 high school students improved their scores on average by 22 points in their second attempt at the SAT mathematics

3. A random sample of 1000 high school students improved their scores on average by 22 points in their second attempt at the SAT mathematics exam. The change in score has standard deviation = 50 (population standard deviation)

a) What is the distribution of sample average SAT score gain? Give a 95% confidence interval for the mean score gain in the population of all students

b) Suppose that a sample of 250 students had produced the sample mean gain of 22 points. Would the 95% confidence interval for the mean score gain , be wider or narrower than the one computed above? (No computations are necessary, explain in words)

c) How large a sample of high school students would be needed to estimate the mean score gain in SAT score to within 2 points with 95% confidence?

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