Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

Exercise 7

Refer to the regression described in Exercise.
a. Do you think that the regression errors plausibly are homoskedastic Explain.
b.
was computed using Equation (5.3). Suppose that the regression errors were homoskedastic: Would this affect the validity of the confidence interval constructed in Exercise (c) Explain.
Exercise
In the 1980s, Tennessee conducted an experiment in which kindergarten students were randomly assigned to "regular" and "small" classes, and given standardized tests at the end of the year. (Regular classes contained approximately 24 students, and small classes contained approximately 15 students.) Suppose that, in the population, the standardized tests have a mean score of 925 points and a standard deviation of 75 points. Let SmallClass denote a binary variable equal to 1 if the student is assigned to a small class and equal to 0 otherwise. A regression of TestScore on SmallClass yields

a. Do small classes improve test scores By how much Is the effect large Explain.
b. Is the estimated effect of class size on test scores statistically significant Carry out a test at the 5% level.
c. Construct a 99% confidence interval for the effect of SmallClass on test score.