A researcher runs an experiment to measure the impact of a short nap on memory. There are 200 participants and they can take a short nap of either 60 minutes or 75 minutes. After waking up, each participant takes a short test for short-term recall. Each participant is randomly assigned one of the examination times, based on the ip of a coin. Let K- denote the number of points scored on the test by the ith participant (0 S K- S 100), let X,; denote the amount of time for which the participant slept prior to taking the test (Xi = 60 or 75), and consider the regression model Yi = [30 + Bin' + ui. a. Explain what the term u i represents. Why will different participants have different values of ui? b. What is E (u ,3 | X)? Are the estimated coefficients unbiased? c. What concerns might the researcher have about ensuring compliance among participants