1. Exercise 9.3: Suppose you are a consultant for a researcher who is interested in investigating the effects of teacher quality on student test scores. Use the strategy of mapping this question to a randomized experiment to help define the question more clearly. Write a memo to the researcher asking for needed clarifications to this study proposal.
2. Exercise 9.4 (a): The table below describes a hypothetical experiment on 2400 persons. Each row of the table specifies a category of person, as defined by his or her pre-treatment predictor x, treatment indicator T, and potential outcomes y0, y1. (For simplicity, we assume unrealistically that all the people in this experiment fit into these eight categories.)
Category #persons.in.category x T y0 y1
1 300 0 0 4 6
2 300 1 0 4 6
3 500 0 1 4 6
4 500 1 1 4 6
5 200 0 0 10 12
6 200 1 0 10 12
7 200 0 1 10 12
8 200 1 1 10 12
In making the table we are assuming omniscience, so that we know both y0 and y1 for all observations. But the (nonomniscient) investigator would only observe x, T, and yT for each unit. (For example, a person in category 1 would have x=0, T=0, y=4, and a person in category 3 would have x=0, T=1, y=6.)
(a) What is the average treatment effect in this population of 2400 persons?
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