00:01
Once again, welcome to the new problem.
00:05
This time we're dealing with inferential statistics.
00:09
We're dealing with inferential statistics.
00:15
And when it comes to inferential statistics, we have hypothesis testing.
00:27
We have hypothesis testing.
00:29
And under hypothesis testing, we have hypothesis testing.
00:33
Testing for proportions and within proportions we have two sample, two sample proportions.
00:45
That's what you're looking for, two sample proportions.
00:48
And the z test for two sample proportions is p -hat 1 minus p -hirt 2, minus p -2, where this becomes zero, because this is the hypothetical.
01:07
Hypothesized difference, hypothesized difference in proportions.
01:17
And of course, we also have the square root of p hat, 1 minus p hat, 1 over n1 over n2.
01:34
And this is the sample for the first proportion and the second one represents the sample for the second proportion.
01:55
So we have the sample for the first proportion and the sample for the second proportion.
02:03
We're looking at a new problem and in this particular problem we have a percentage of of customers and these customers happen to be leaving the store with some parches and the understanding is that the percentage of women living the store with the patches is lower than the percentage of men.
02:30
So we have a random sample and one is 180 female shoppers and x1 is 140 female shoppers and x1 is 145 left with purchases and then for the males we have in 270 male shoppers in 135 left with the purchase so at alpha equals to 0 .10 we want to determine if the percentage of females or women leaving the store with the purchase is lower than the percentage of men so that's what we want to we want to determine the now and alternative hypothesis and also we want to determine the test statistic.
03:24
So coming back to this problem, the now hypothesis is p1 equals to p2.
03:32
These are the two proportions and therefore we can write this as p1 minus p2 equals to zero.
03:40
So that's one aspect of the problem.
03:44
And then the alternative hypotheses, the alternative hypotheses is, so it's the opposite.
03:54
So this is the opposite.
03:55
So we put greater than right there.
03:58
And so this is also going to be greater than right there.
04:01
The alternative hypotheses is that p1 is less than p2, or we can write it as p1 minus p2, is less than zero.
04:15
The test statistic happens to be the z test, and so we have z equals to p -hat -1 minus p -hat -2, all of a radical p -hat -1 minus p -hat, 1 over n1 plus 1 over n2...