Question

The state of California conducted an experiment with college students. Teachers and students were randomly assigned to be in a regular sized class or a small sized class. The dependent variable is the student’s score on a math test (MATHSCORE). Let SMALL = 1 if the student is in a small class and SMALL = 0 otherwise. The other variable of interest is the number of years of teacher experience, given by TCHEXPER. Let BOY = 1 if the stu- dent is male and BOY = 0 if the student is female.

a) (5 points) Write down the model for the dependent variable MATHSCORE as a function of SMALL, TCHEXPER, BOY and BOY*TCHEXPER, with pa-

rameters β1 , β2 , β2 , ... etc.

b) (5 points) What is the expected math score for a male student in a small class with a teacher having 10 years of experience? (Your answer will be in terms of the model parameters, including βi’s).

c) (5 points) What is the change in the expected math score for a male student

in a small class with a teacher having 11 years of experience rather than 10? d) (5 points) State the marginal effect of teacher experience on expected math scores.
e) (5 points) State, in terms of model parameters, the null hypothesis that the marginal effect of teacher experience on expected math score does not
differ between men and women, against the alternative that men benefit
more from teacher experience.

Answer 1

(a)

b)

For a male student in a small class with a teacher having 10 years of experience is

BOY = 1, SMALL = 1, TCHEXPER = 10

The expected math score for a male student in a small class with a teacher having 10 years of experience is,

c)

The expected math score for a male student in a small class with a teacher having 11 years of experience is,

The change in the expected math score for a male student in a small class with a teacher having 11 years of experience rather than 10 is,

d)

The marginal effect of teacher experience on expected math scores is,

e)

For men, (BOY = 1), the marginal effect of teacher experience on expected math scores is

For women, (BOY = 0), the marginal effect of teacher experience on expected math scores is

The difference in the marginal effect of teacher experience on expected math scores between men and women is

The null and alternative hypothesis are,