00:01
So we have a binomial experiment with n1 in the first trial, 75, 45 successes.
00:12
And the second experiment, same size of 165 successes.
00:16
And we want to test at the 5 % level of significance to claim that the probabilities of success for the two binomial experiments differ.
00:26
So let's go ahead and state those.
00:30
It's going to be here.
00:31
I have it written here the h -not, the null, is that the two proportions are equal, p1 equals p2, and the alternative is going to be, it's going to be the complement of that, that they're not equal.
00:52
This p1 not equal to p2, that is what we interpret this, this phrase in notation.
01:04
Testing the claim that the probabilities of success the two binomial experiments differ.
01:09
They're not equal.
01:14
Now i want to get the pooled probability of success for the two experiments.
01:18
So the pooled probability is equal to, and i'll do pl for pooled.
01:25
It's x1 or r1, i guess, because we're using r1 plus r2 all over n1 plus n2.
01:34
So we take the point.
01:35
Total successes add them up divided by the sum of the total unit sample and take that ratio so it's 110 over 175 and the pooled portion values this.
01:50
6285714286 and the distribution the excuse me what does the sample statistic follow it's going to follow the standard normal because the number of trials is sufficiently large even teeth t tests get large enough and the t values themselves basically becomes z scores when you get over as like as you get closer to a total of 200 they're very very close to z scores so there we go and let's go ahead and run through this so our statistic is given the following way it's p1 minus p2 all over the square root of the pooled proportion times one minus the pool proportion times one over the sample size of one plus one over the sample size of two.
03:07
And that is gonna be our z score calculator.
03:15
And as i'm doing this, i'm recognizing it made a mistake...