A Subsample from the Current Population Survey Is Taken, on Weekly

Essay

A subsample from the Current Population Survey is taken, on weekly earnings of individuals, their age, and their gender. You have read in the news that women make 70 cents to the $1 that men earn. To test this hypothesis, you first regress earnings on a constant and a binary variable, which takes on a value of 1 for females and is 0 otherwise. The results were: $\widehat{ E a m }$ = 570.70 - 170.72 × Female, R²=0.084, SER = 282.12.
(9.44)(13.52)
(a)Perform a difference in means test and indicate whether or not the difference in the mean salaries is significantly different. Justify your choice of a one-sided or two-sided alternative test. Are these results evidence enough to argue that there is discrimination against females? Why or why not? Is it likely that the errors are normally distributed in this case? If not, does that present a problem to your test?
(b)Test for the significance of the age and gender coefficients. Why do you think that age plays a role in earnings determination?