Using the data in GPA2, the following equation was estimated:

sat 5 1,028.10 1 19.30 hsize 2 2.19 hsize2 2 45.09 female 16.292 13.832 1.532 14.292 2 169.81 black 1 62.31 female#

black 112.712 118.152 n 5 4,137, R2 5 .0858.

The variable sat is the combined SAT score; hsize is size of the student’s high school graduating class, in hundreds; female is a gender dummy variable; and black is a race dummy variable equal to one for blacks, and zero otherwise.

(i) Is there strong evidence that hsize2 should be included in the model? From this equation, what is the optimal high school size?

(ii) Holding hsize fixed, what is the estimated difference in SAT score between nonblack females and nonblack males? How statistically significant is this estimated difference?

(iii) What is the estimated difference in SAT score between nonblack males and black males? Test the null hypothesis that there is no difference between their scores, against the alternative that there is a difference.

(iv) What is the estimated difference in SAT score between black females and nonblack females?

What would you need to do to test whether the difference is statistically significant?