A statistical study of 430 high school seniors gained an average of x = 15 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation o = 40. We want to estimate the mean change in score u in the population of all high school seniors. (a) Give a 95% confidence interval foru based on this sample. Round your answers to two decimal places. 13.93 x to 43.93 (b) Based on your confidence interval in part (a), how certain are you that the mean change in score u in the population of all high school seniors is greater than zero? 0% O 68% 95% 99.7% 100%

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