Problem Four. Consider the following situation. There are $800$ new employees enrolled in a lab$-$in$-$the$-$field experimental study at an inbound call sales center. The employees do not realize they are part of an experiment. This experiment is designed to see how effective workplace mentorship programs are at increasing the productivity of new employees.

a$)$ Let us consider worker $i.$ Let $Y_i$ be the average daily revenue that worker i earns for the sales center. Worker i can either be enrolled in the treatment group and be given a mentor or the control group and not given a mentor. Let $Y_i^{\text{T}\text{r}\text{e}\text{a}\text{t}\text{m}\text{e}\text{n}\text{t}}$ be worker $i\text{'}$s average daily revenue if they are given a mentor. Let $Y_i^{\text{C}\text{o}\text{n}\text{t}\text{r}\text{o}\text{l}}$ be worker $i\text{'}$s average daily revenue if they are not given a mentor. Argue that for a given worker $i$ we can only ever observe $Y_i^{\text{T}\text{r}\text{e}\text{a}\text{t}\text{m}\text{e}\text{n}\text{t}}$ or $Y_i^{\text{C}\text{o}\text{n}\text{t}\text{r}\text{o}\text{l}}$ and it is not possible to observe both.