In the move to online instruction due to COVID-19, Development University was concerned that its students may not have the technology they needed at home to keep up with their classes. In order to address this issue, at the start of the term, the University offered all students coupons for a 50% price discount on a new iPad. The hope was that the iPad would allow students to participate more fully in their online classes, and therefore allow them to learn more.

Development University heard that you have learned how to do impact evaluation in your economics classes, so asked you to evaluate how well the iPads worked for their students. In particular, they wanted to know if the iPads caused student grades to improve. In looking at the data, you notice that although all students were offered the coupon, only half of them purchased an iPad through the program. Therefore, you decide to compare the average GPAs of students who purchased an iPad to those who didn't. You find that students who purchased an iPad had an average GPA of 3.6, and students who did not purchase an iPad had an average GPA of 3.0.

A. Briefly in a sentence describeyoi?in the context of this study. Your answer should clearly define the treatment and the outcome variable in this study, not just the abstract language of whatyoi means in general.

B.Briefly in a sentence that clearly describesE[y1i|Di= 0]in the context of this study. Again, your answer should demonstrate that you have a clear understanding of both the treatment and the outcome variable in this study.

C. Write an equ'n (in expectations notation) that represents yourobservedestimate of the average effect of the iPads on student grades. As described above, your estimate is the difference in grades between those who purchased an iPad and those who didn't. (Note: if you are unable to answer using subscripts, it's ok to answer in normal-sized script. For example, E[Y0i | Di=0].)

D.Calculate the ATE using the GPAs provided. Is this estimate the True Average Treatment Effect (ATE)? Why or why not?

E.Do you expect selection bias to be positive, negative, or zero in this case? answer should be consistent with how the data was collected.

F.Briefly explain one potential cause of selection bias. Your answer should demonstrate that you have a clear understanding of selection bias and what would cause it.

G.Due to your concerns, Development University decides to conduct a randomized control trial with incoming students in the fall. That is, incoming students are randomly assigned to either receive the same 50% coupon as before for a discounted iPad, or to not receive a coupon. Will this research design allow you to estimate the true Average Treatment Effect of iPads on student performance? Why or why not?

H. briefly describe one concern you may still have with this randomized design.

thank you for any help :)