Improving SAT scores. Refer to the Chance (Winter 2001)

Improving SAT scores. Refer to the Chance (Winter 2001)

Improving SAT scores. Refer to the Chance (Winter 2001) examination of SAT scores of students who pay a private tutor to help them improve their results, presented in Exercise 2.105 (p. 73). On the SAT-Mathematics test, these students had a mean change in score of +19 points, with a standard deviation of 65 points. In a random sample of 100 students who pay a private tutor to help them improve their results, what is the likelihood that the change in the sample mean score is less than 10 points?
Exercise 2.105
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.
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 SAT Math or SAT-Verbal, is the one most likely to have had the 140-point increase? Explain.

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