Suppose that you are asked to conduct a study to

Suppose that you are asked to conduct a study to determine whether smaller class sizes lead to improved student performance of fourth graders.
(i) If you could conduct any experiment you want, what would you do? Be specific.
(ii) More realistically, suppose you can collect observational data on several thousand fourth graders in a given state. You can obtain the size of their fourth-grade class and a standardized test score taken at the end of fourth grade. Why might you expect a negative correlation between class size and test score?
(iii) Would a negative correlation necessarily show that smaller class sizes cause better performance? Explain.