3. Suppose that you are interested in the relationship between the height of children and that of their parents. To do some research on this problem, you collect data from 110 college students and estimate the following linear regression Studenth = 19.6 + 0.73 x Midparh, R2 = 0-45- (72) (0.10) With ESS = 2.0 and where Studenth is the height of students in inches, and Midparh is the average of the parental heights. Values in parentheses are the standard errors. (a) Test the null hypothesis that average parental height has no effect on the height of their children versus the alternative hypothesis that there is a non-zero effect. Carefully state the null and alternative hypotheses in terms of hypotheses concerning the parameters All Rights Reserved of the linear model, and carry out a test at the 5% significance level (use 1.96 as critical value) (b) Construct a 95% confidence interval for the slope coefficient of the regression above. (C) Is the result in part (b) consistent with the test result obtained in part (a)? Explain your answer carefully