An SRS of 450 high school seniors gained an average of X = 20 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation & = 49. You can find the critical values to three decimal places by using the last row in table C. (a) Find a 95% confidence interval for the mean change in score y in the population of all high school seniors. (Enter your answers rounded to two decimal places.) [ | lower bound of confidence interval: upper bound of confidence interval: L (b) What is the margin of error for 95% ? (Enter your answer rounded to two decimal places.) margin of error: | (c) Suppose we had an SRS of just 100 high school seniors. What would be th (c) Suppose we had an SRS of just 100 high school seniors answer rounded to three decimal places.) (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? _) Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation also decrease. _J) Decreasing the sample size decreases the margin of error, provided the confidence level and population standard deviation remain the same. _) Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same. ) Decreasing the sample size keeps the margin of error the same, provided the confidence level and population standard deviation remain the same