4. Suppose that Col.GPA = Bo + BIPC + U, where Col_GPA denotes the student's college GPA and PC is a binary variable with PC = 1 if the student owns a PC and PC = 0 otherwise. Define noPC as a dummy variable for whether the student does not own a PC, with noPC=1 if the student does not own a PC and noPC-0 if the student does own a PC. Suppose that, in the data, there are 34 students who do not own a PC and 53 students who own a PC. The sample average of Col GPA for those students without a PC is 2.5, and the sample average of Col GPA for those students with a PC is 3.5. Suppose further that, in the data, the sample standard deviation of Col_GPA for those students without a PC is .62, and the sample variance of Col_GPA for those students with a PC is .47. (a) What are the OLS estimates of Bo and Bi? Why can you compute them in this fashion? (b) Test Ho : Bi 0 at the 5% significance level. What is the p-value for this hypothesis test? What do you conclude? (c) Suppose that the researcher instead wishes to do an OLS regression of Col_GPA on noPC. What would be the resulting OLS estimates for that regression