It is possible that any differences we are seeing in the salaries ofthe male Professors are simply due to random chance differences in the men and women we sampled in this data. So before we make any real conclusions here, it is important to test the data.

Run an appropriate Wilcoxon Test in R to determine if salary is stochastically different for one of thegenders of Professors. (The professors in this data will act as a representative sample for the population of professors from all universities.) Use the significance level of=0.05=0.05for your test.

Your Answer

Type of test: Wilcoxon Rank Sum (Mann-Whitney) TestWilcoxon Signed-Rank TestWilcoxon Rank Sum (Mann-Whitney) Test

Test statistic:

P-value:

Conclusion: Reject the null.Fail to reject the null.Fail to reject the null.

Correct

Your Answer:Fail to reject the null.

There is sufficientinsufficientinsufficient evidence to conclude thatsalary is stochastically different for one of thegenders of professors. In looking back at our numerical summaries and graphical summary, we see that it appears that male Professors are being paid a median salary that is $ more than the median female salary. Further research into why this discrepancy exists would be warranted though this discrepancy itself does not prove anything further than a pay gap in median salaries of Professors. We can't claim that discrimination or any other reason in particular has caused the pay gap without further research. But this difference certainly warrants further research into the "why" behind the gap. The gap has been shown to exist by the analysis above. We just don't have any explanation as to why it is there.