Prior to getting to the authors' experiment, suppose we were interested in providing a credible answer to the following general question: \"Does providing students with nancial incentives to do well on tests improve test performance?\" A friend of yours proceeds to answer this question by going to a local high school and collecting performance data on student tests. Your friend then surveys the parents of all students in her sample, asking parents, \"On the day of the last test your child wrote, did you promise to pay him or her at least $10 if they improved their performance relative to the last time they took a similar test?\" Based on the answers to her survey, your friend creates the following grouping variable for your sample of 72 = 1,. . . , N students: D _ 1 if parents promised to pay 1 0 if parents did not promise to pay. She then species the following econometric model to describe the test score performance of student 2': Y, =J80+JBIDt+U (a) Provide an example of a factor that could be in U,. (b) Explain (in words) why it is problematic to simply compare conditional means as way of answering the research question. That is, why is it not a good idea to compare the mean test score of students with D,- = 1 to the mean test score of students with D,- = 0? (c) Use the econometric model above to show (mathematically) how a comparison of conditional means is biased by selection