You Have Collected 14,925 Observations from the Current Population Survey

You have collected 14,925 observations from the Current Population Survey. There are 6,285 females in the sample, and 8,640 males. The females report a mean of average hourly earnings of $16.50 with a standard deviation of $9.06. The males have an average of $20.09 and a standard deviation of $10.85. The overall mean average hourly earnings is $18.58.
a. Using the t-statistic for testing differences between two means (section 3.4 of your textbook), decide whether or not there is sufficient evidence to reject the null hypothesis that females and males have identical average hourly earnings.
b. You decide to run two regressions: first, you simply regress average hourly earnings on an intercept only. Next, you repeat this regression, but only for the 6,285 females in the sample. What will the regression coefficients be in each of the two regressions?
_{c. Finally you run a regression over the entire sample of average hourly earnings on an intercept and a binary variable DFemme, where this variable takes on a value of 1 if the individual is a female, and is 0 otherwise. What will be the value of the intercept? What will be the value of the coefficient of the binary variable?
d. What is the standard error on the slope coefficient? What is the t-statistic?
e. Had you used the homoskedasticity-only standard error in (d)and calculated the t-statistic, how would you have had to change the test-statistic in (a)to get the identical result?}