23 Improving SAT scores. Chance (Winter 2001) and National Education Longitudinal Survey (NELS) performed a study of 265 students who paid a private tutor to help them improve their SAT scores. The changes in both the SATMathematics and SAT-Verbal scores for these students are reproduced in the following table:

a. Construct and interpret a 95% confidence interval for the population mean change in SAT-Mathematics score for students who pay a private tutor.

b. Repeat part a for the population mean change in SATVerbal score.

c. Suppose the true population mean change in score on one of the SAT tests for all students who paid a private tutor is 15. Which of the two tests, SAT-Mathematics or SAT-Verbal, is most likely to have this mean change?
Explain.

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Mean change in score Standard deviation of score changes SAT-Math SAT-Verbal 19 7 65 49