91Ó°ÊÓ

Retaking the SAT. In Exercise 16.2 (page 377), we saw that an SRS of 400 high school seniors gained an average of \(x^{-} x=9\) points in their second attempt at the SAT Mathematics exam. Assuming that the change in score has a Normal distribution with standard deviation \(\sigma=40\), we computed a \(95 \%\) confidence interval for the mean change in score \(\mu\) in the population of all high school seniors. (a) Find a \(90 \%\) confidence interval for \(\mu\) based on this sample. (b) What is the margin of error for \(90 \%\) ? How does decreasing the confidence level change the margin of error of a confidence interval when the sample size and population standard deviation remain the same? (c) Suppose we had an SRS of just 100 high school seniors. What would be the margin of error for \(95 \%\) confidence? (d) How does decreasing the sample size change the margin of error of a confidence interval when the confidence level and population standard deviation remain the same?