Improving SAT scores. The National Education Longitudinal Survey (NELS) tracks a nationally representative sample of U.S. students from eighth grade through high school and college. Research published in Chance (Winter 2001) examined the SAT scores of 265 NELS students who paid a private tutor to help them improve their scores. The table summarizes the changes in both the SAT-Mathematics and SAT-Verbal scores for these students.

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

a. Suppose one of the 265 students who paid a private tutor is selected at random. Give an interval that is likely to contain the change in this student’s SAT-Math score.

b. Repeat part a for the SAT-Verbal score.

c. Suppose the selected student’s score increased on one of the SAT tests by 140 points. Which test, the SATMath or SAT-Verbal, is the one most likely to have had the 140-point increase? Explain.