please answer part e. (e) Upon further investigation of pre-treatment characteristics among your sample, you find that there is an unusually large amount of math majors in the control group. You know for a fact that these students tend to be very good at math (i.e., they tend to have higher grades). Furthermore, a test similar to the one in the previous part confirms that the amount of math majors between the treatment and control groups is unbalanced.i. (3 points) Here, you seem to have a selection bias issue. And indeed, this could occur when the solution you proposed in part (b) ends up not working out. What sign would you expect the selection bias to be (i.e., is it positive or negative)? And what does the sign tell you about how ??OLS estimates the ATT? Please keep your response concise.ii. (4 points) To alleviate the selection bias issue described above, you consider altering your regression model from part (c). Clearly explain how you would do so to address this issue, and write down your new regression specification . Also, discuss how your solution will affect the estimate, ??OLS. Hint: Assume you have data on your student participants' college majors.

2. Selection Bias. Let Y, be some outcome variable for an individual i and D, be a binary variable that takes on a value of "1" if the individual receives some treatment. Recall the following potential outcomes framework: Y, = (0) , if D, = 0 (1) , if D, = 1 where y (1) is the observed outcome for those that receive the treatment while y(0) is the outcome for those that did not receive it. Thus, Y, = Digi(1) + (1 - D.)y>(0). In this framework, we estimate E(Y,|D, = 1) - E(Y|D, = 0)