The Professor's Response
Good evening Professor,
As I was doing Problem 3, from section 9.4 of the videos I noticed the following:
You had used the mean of men first then the mean of women in the claim giving you : Mu(m) Mu(m)
This lead to my alternative hypothesis being: Ha: Mu(w)> Mu(m)
Because of this when i got the test stat value of -7.5926, it would have landed on the left side of my bell curve, when my rejection region was on the right tail. I know since it is such a big number we initially suppose we will reject Ho, but I was wondering if it mattered in this case whether we began with men instead of women, since by starting with women like I did would lead to support Ho and reject Ha.
See the professor's answer below.
Hi Mabel,
Your Ha would require a right-tailed test which would mean your negative test statistic would not cause rejection of the null hypothesis. This would give you a different conclusion from what I derived doing the problem correctly. It is not wrong to express your claim as you did, but you did not follow the rule of being consistent in the order in which you do things after the claim.
If you write a claim placing the mean for men first, then the sample mean for men must be entered into your test statistic formula first as well. If you place the mean for women first in your claim, then you need to place the sample mean for women first in your test stat formula. Watch the video below for more explanation.
Incidentally, I hope you are doing all of the homework for each section not just the problems that have videos devoted to them.
Sincerely,
Professor McGuckian