Suppose a researcher, using wage data on 250 randomly selected male workers and 280 female workers, estimates the OLS regression

\[ \begin{equation*} \widehat{\text { Wage }}=12.52+2.12 \times \text { Male, } R^{2}=0.06, S E R=4.2 \tag{0.23} \end{equation*} \]

where Wage is measured in dollars per hour and Male is a binary variable that is equal to 1 if the person is a male and 0 if the person is a female. Define the wage gender gap as the difference in mean earnings between men and women.

a. What is the estimated gender gap?

b. Is the estimated gender gap significantly different from 0? (Compute the \(p\)-value for testing the null hypothesis that there is no gender gap.)

c. Construct a \(95 \%\) confidence interval for the gender gap.

d. In the sample, what is the mean wage of women? Of men?

e. Another researcher uses these same data but regresses Wages on Female, a variable that is equal to 1 if the person is female and 0 if the person a male. What are the regression estimates calculated from this regression?

\[ \widehat{\text { Wage }}=\ldots+\ldots \times \text { Female, } R^{2}=\ldots, S E R= \]