In 1985, the state of Tennessee carried out a statewide experiment with primary school students. Teachers and students were randomly assigned to be in a regular-sized class or a small class. The outcome of interest is a student's score on a math achievement test (MATHSCORE). Let \(S M A L L=1\) if the student is in a small class and \(S M A L L=0\) otherwise. The other variable of interest is the number of years of teacher experience, TCHEXPER. Let \(B O Y=1\) if the child is male and \(B O Y=0\) if the child is female.

a. Write down the econometric specification of the linear regression model explaining MATHSCORE as a function of SMALL, TCHEXPER, BOY and BOY \(\times\) TCHEXPER, with parameters \(\beta_{1}, \beta_{2}, \ldots\)

i. What is the expected math score for a boy in a small class with a teacher having 10 years of experience?

ii. What is the expected math score for a girl in a regular-sized class with a teacher having 10 years of experience?

iii. What is the change in the expected math score for a boy in a small class with a teacher having 11 years of experience rather than 10 ?

iv. What is the change in the expected math score for a boy in a small class with a teacher having 13 years of experience rather than 12 ?

v. State, in terms of the model parameters, the null hypothesis that the marginal effect of teacher experience on expected math score does not differ between boys and girls, against the alternative that boys benefit more from additional teacher experience. What test statistic would you use to carry out this test? What is the distribution of the test statistic assuming then null hypothesis is true, if \(N=1200\) ? What is the rejection region for a \(5 \%\) test?

b. Modify the model in part (a) to include SMALL \(\times B O Y\).

i. What is the expected math score for a boy in a small class with a teacher having 10 years of experience?

ii. What is the expected math score for a girl in a regular-sized class with a teacher having 10 years of experience?

iii. What is the expected math score for a boy? What is it for a girl?

iv. State, in terms of the part (b) model parameters, the null hypothesis that the expected math score does not differ between boys and girls, against the alternative that there is a difference in expected math score for boys and girls. What test statistic would you use to carry out this test? What is the distribution of the test statistic assuming the null hypothesis is true, if \(N=1200\) ? What is the rejection region for a \(5 \%\) test?