Question

Using data on a representative sample of college students, the following model was estimated: (standard errors are in parentheses) sat =1,028.1+19.3hsize − 2.2hsize2 − 45.1Female −169.8black + 62.3 female*black (6.29) (3.83) (0.53) (4.29) (12.7) (18.15) n = 4,137 and ? 2= 0.0858 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 equal to one for females and zero otherwise, and black is a race dummy variable equal to one for blacks and zero otherwise.

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

Answer 1

The regression equation estimated on the data is:

sat =1,028.1+19.3hsize − 2.2hsize2 − 45.1Female −169.8black + 62.3 female*black

Assuming that hsize is held constant, we know that there will indeed be a difference in the SAT score between nonblack females and non blank males. The only variable that will affect the score for non black females and non black males is the 'female' variable. The coefficient is -45.1. Thus, the estimated difference in the scores of non black males and non black females is 45.1 Females are estimated to have a score 45.1 less than males (males score more than females; difference is 45.1).

The test statistic would be the estimate divided by the standard error.

Thus, test statistic= -45.1/4.29= -10.51282.

Thus, since this is a very large test statistic, we know that this will be on the tail of the distribution. Thus, the difference is very statistically significant, even at high significance levels.