A professor decides to run an experiment to measure the effect of time pressure on final exam scores. He gives each of the 400 students in his course the same final exam, but some students have 90 minutes to complete the exam while others have 120 minutes. Each student is randomly assigned one of the examination times based on the flip of a coin. Let Yi denote the number of points scored on the exam by the ith student (0 ≤ Yi ≤ 100), let Xi denote the amount of time that the student has to complete the exam (Xi = 90 or 120), and consider the regression model Yi = β0 + β1Xi + ui.
a. Explain what the term u-t represents. Why will different students have different values of ui?
b. Explain why E(ui | Xi) = 0 for this regression model.
c. Are the other assumptions in Key Concept 4.3 satisfied? Explain.
d. The estimated regression is Ŷi = 49 + 0.24 Xi.
i. Compute the estimated regression's prediction for the average score of students given 90 minutes to complete the exam. Repeat for 120 minutes and 150 minutes.
ii. Compute the estimated gain in score for a student who is given an additional 10 minutes on the exam.