00:01
So we have a veterinarian that's interested in researching the proportion of men and women who own cats.
00:05
And this vet believes that men cat owners, the proportion of men cat owners is smaller than the proportion of women cat owners.
00:13
So our null hypothesis would be that p, what we'll call men, yeah, we'll do p sub m for the proportion of men.
00:25
Well, that would be greater than or equal to the proportion of women.
00:28
The alternative hypothesis is that proportion of men is less than proportion of women and we're going to test this at the alpha of 0 .10 level of significance and we're going to use a two proportion z -test and that z -score for those z -test is going to give us a p -value and the rule is if our p -value that we get is less than the alpha we're going to reject.
00:54
So reject if, reject h naught, if our alpha, if our p -value is less than our alpha.
01:03
Alright so let's go ahead and verify that we can in fact do this.
01:07
The first thing we need to do for a two sample proportion test is that our sample of men and women, n, so n, n, and likewise n, n, n, and w for women.
01:26
That needs to be less than 5 % of all men and all women respectively.
01:31
And that's a reasonable assumption that there's more than 60 is less than 5 % of all the men and 80 is less than 5 % of all men.
01:38
So that's a reasonable assumption.
01:39
The other thing we need to do is verify that n times p -hat, the proportion estimate, times 1 minus the proportion estimate is greater than or equal to 10.
01:53
And it is, it's true.
01:58
And please be aware that there's something we need to do here, this p hat.
02:07
We have two proportions that we can get already.
02:09
And we, well, these are other proportions.
02:11
There's 60 men that were selected, 80 women, and the proportion, this is the p hat values for men and women respectively.
02:17
So pi for men and women.
02:21
But this other p -hat variable, p -hat, p -hat is the proportion estimate of, is the pool proportion, so it's xm plus xm, sorry, xm plus xw, the number of men who had cats, and the number of women who had cats in the sample.
02:47
Divide by the total sample size, n plus w.
02:52
So we have the denominator 60 and 80, that's not a problem.
02:57
We just need to figure out how many were here.
03:00
How many men and women that was.
03:01
Well what we do is take 25 % times 60, 50 % times 80.
03:05
We have these values 50 and 40.
03:13
So this gives us, what's that, 55 over 140.
03:18
That's our pooled proportion.
03:19
That's what p -hat is...