A study looked at the 50 states in the United States and compared educational spending per student in each state with the average score on college entrance examination tests (the SAT and ACT). There is a positive correlation across states in spending per student and in the percentage of students taking college entrance examination tests.

a. Explain why high school seniors who take the SAT (or ACT) are not a random sample of all high school seniors.

b. Do you think that the average test score in a state would tend to increase or decrease if a larger percentage of the state’s students took college entrance examination tests?

c. Suppose that your answer to

(b) is correct and, also, that educational spending has no effect at all on test scores. Explain why we would observe either a positive or negative statistical relationship between spending and average test scores.