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: $\begin{aligned} \widehat{\text { Earn }}= & 570.70-170.72 \times \text { Female }, R^{2}=0.084, \text { SER }=282.12 . \\& (9.44)\quad(13.52)\end{aligned}$
(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?