Question 3 (33 pts.) Michael is a health economics student interested in estimating the effect of health insurance coverage Di on the number of doctor visits Y, by estimating the population regression function (PRF) YP,+ 2D,u by using the sample reported in Table 2. Enrollment in a health insurance plan is voluntary. Table 2 Michael has heard that observational studies produce biased results, while randomized experiments deliver the causal effect if an exhaustive set of samples are produced. He conducts a set of experiments, which are accurately reported in Table 3. However, Michaels grasp of the analysis of randomized experiments is somewhat shaky and he needs assistance in answering a set of questions Table 3 Treatment Control Sample 2 Sample 3 Sa d) Selection bias: i. (2 pts.) Define the selection bias using appropriate mathematical notation. ii. (2 pts.) Interpret each of the two terms in the selection bias by specifying the relevant group, the state of nature and the outcome of interest ii.(1pt.) Describe what the two terms of the selection bias are comparing. iv. (2 pts.) Compute the selection bias. In your answer, first expand each expected value by using the appropriate letters and subscripts for each observation and then substitute the corresponding numerical values.