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.