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The results of a study of 251 students who paid a private tutor to help them improve their scores on a standardized test are shown below. The changes in both the Mathematics and Verbal scores for these students are reproduced in the table. Complete parts a through c below.

Test_score_improvements                   Math   Verbal

Mean_change_in_score                           22           10

Standard_deviation_of_score_changes   66           49

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

b) Construct and interpret a? 95% confidence interval for the population mean change in the Verbal score for students who pay a private tutor

c) Suppose the true population mean change in score on one of the standardized tests for all students who paid a private tutor is 12. Which of the two? tests, Mathematics or? Verbal, is most likely to have this mean? change? Explain.

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