3. In a hypothetical study of SAT scores one year, the ETS computes the average score Math and Verbal SAT scores for each of the 50 states and D.C., as well as the percentage of high-school seniors taking the test in each state (and in D.C.). The correlation between the average Math SAT scores and the percentage of students taking the test was −0.76.
(a) (3 pts) True or False: Scores tend to be lower in states where a higher percentage of students take the test. If you answered true, explain why this makes sense. If you answered false, explain what accounts for the negative correlation.
(b) (2 pts) The average Math SAT score in South Dakota was higher than the average Math SAT score in New York. Does the data show that high schools in South Dakota do a better job teaching math than high schools in New York, or is a different explanation possible?
(c) (3 pts) As part of the study described above, the ETS also computed the correlation between the average Verbal and Math SAT scores across the 50 states and D.C., and found that it was about 0.88. Would the correlation between the Math SAT and Verbal SAT scores of individualstudents across the U.S. be higher than 0.88, lower than 0.88 or about the same as 0.88? Explain your answer briefly.
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