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 SMALL \(=1\) 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.

a. Write down the econometric specification of the linear regression model explaining MATHSCORE as a function of SMALL and TCHEXPER. Use \(\beta_{1}, \beta_{2}\), and \(\beta_{3}\) as the model parameters. In this model, what is the expected math score for a child in a regular-sized class with a teacher having 10 years of experience? What is the expected math score for a child in a small class with a teacher having 10 years of experience?

b. Let \(B O Y=1\) if the child is male and \(B O Y=0\) if the child is female. Modify the model in part (a) to include the variables \(B O Y\) and \(B O Y \times S M A L L\), with parameters \(\theta_{1}\) and \(\theta_{2}\). Using this model 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 null hypothesis, written in terms of the model parameters, that the sex of the child has no effect on expected math score? What is the alternative hypothesis? What is the test statistic for the null hypothesis and what is its distribution if the null hypothesis is true? What is the test rejection region for a \(5 \%\) test when \(N=1200\) ?

iv. It is conjectured that boys may benefit from small classes more than girls. What null and alternative hypothesis would you test to examine this conjecture?