 �One of our board members told me he is concerned that there is not enough diversity in our programming departments in some of the fast technology�s offices.� �Really? Was he just reacting to the news reports about our industry?� �No. Specifically, he said he has heard complaints that fast technologies women programmers earn less than male programmers, and that women are underrepresented in the management ranks in the programming department.� �I doubt that. We have made a concerted effort to hire women programmers the last two years and I'm sure we pay them competitive salaries.� �Perhaps. But we need to be sure we are. Could you run some analysis and let me know what the real situation is?� �Sure. I will get right on it. Well, it has been a day since I asked Brenda in HR to collect some data and see if there is a difference in the salaries of male and female programmers. I'll go see what she has come up with. Brenda, I hope you have some good news for me.� �Well, I have some good news and some not so good news.� �Darn. Tell me what you found out.� �Remember I had to get a sample of the programmer salaries because we have so many offices.� �Yes, it would be nice to get all the salary info, but I understand.� �Well, initially I was able to get the salaries for 31 male and 18 female programmers. The mean salary for the males is $81,188 and the mean salary for females is $68,974.� �Wow. That is a big difference.� �Yes, but remember we have to take into consideration the variations as well when we run the hypothesis test to see if there is a statistically significant difference.� �Yes, I remember that, from my business statistics class, that is a plug for this course.� �This is a screenshot of the two sample t-test I ran using Excel. Because the sample standard deviations are similar, I used an equal variances test with a hypothesized mean difference of $0.� �But aren�t we okay? The p-value is 0.164 which is a lot larger than 5 percent.� �Yes, but that is for a non-directional test. Remember, Kwanee said the board member claimed males are paid more, so you have to use the one-tail or directional p-value.� �I remember. Paid more would be a greater than symbol, and that is a form of inequality.� �Exactly. This is a right-tail test. The claim is the alternative, the mean-male salary is greater than the mean-female salary. Or, as I prefer, the mean difference between the male and female salaries is greater than 0.� �Okay, but the p-value is still greater than 0.05, and that means there is no statistical difference. Right? �Yes, the p-value of 0.082 is larger than 5 percent, but the test statistic of 1.414 is not that far from the critical value of 1.678. Don't worry me because of the small sample size I initial had.� �Does the sample size, really, make that much difference? �Yes, it sure does. Remember when we do these calculations, we use the standard error and not the simple standard deviation. The standard error is equal to the standard deviation divided by the square root of the sample size. That causes the standard error to rapidly get smaller as the sample size gets larger.� �Okay, I recall that now. But I never really understood why you divide by the square root of the sample size.� �I can give you a link to a great video showing why that is true. See the link in the module notes. I was able to double the sample size this morning just before you came in.� �How does it look?� �That is the bad news. With the additional information, the right tail p-value is 0.026, which is a lot smaller than 5 percent.� �Shucks. That is statistically significant. But is the difference of practical significance?� �Yes, the test statistic, the main difference, is almost $12,000.� �Ouch. I guess I better inform Connie.� �Better you than me. I don't think she will be happy.� �True, but now that we know we have a problem, we can begin to take steps to correct it.�