Suppose that a researcher, using data on class size (CS) and average test scores from 100 third-grade classes, estimates the OLS regression and obtain the following results (standard errors in parenthesis): =520.45.82 (20.4) (2.21) a) A classroom has 22 students. What is the regression's prediction for the classroom's average test score? b) Last year a classroom had 19 students, and this year it has 23 students. What is the regression's prediction for the change in the classroom average test score? c) The sample average class size across the 100 classroom is 21.4. What is the sample average of the test scores across the 100 classrooms? d) Construct a 95% confidence interval for , the regression slope coefficient. e) Is the estimated effect of class size on test scores statistically significant? Carry out a two- sided test of the null hypothesis 0: = 0. Do you reject the null hypothesis at the 5% level? At the 1% level? f) Carry out the two-sided test of the null hypothesis 0: =5.6. Without doing any additional calculations, determine whether -5.6 is contained in the 95% confidence interval for . g) Construct a 99% confidence interval for , the intercept.