00:01
For this problem, we have that the null hypothesis would be that the population proportion is still equal to 0 .52, 52%.
00:07
The alternate hypothesis is simply that the proportion has changed, so p does not equal 0 .52.
00:15
We are testing to see, or we are doing the hypothesis test here at the alpha equals 0 .1 level of significance.
00:24
So the approach that i'll take, let's see, yeah, we're using a critical value approach for a two -tailed test.
00:30
So the approach that i'll take, i'll just write out a rejection region.
00:35
I'm not trying to go through the exact steps sort of in the order that you have there, just because the formatting is a little bit messed up, but i will make sure to hit all of the steps as we go along.
00:47
We will reject the null hypothesis if the magnitude of our observed z -score is greater than the z -score for a tail proportion of alpha over 2.
01:00
So that's the z -score for a tail proportion of 0 .05, which i can find using my table of values over here.
01:07
So we want a one -tailed proportion of 0 .05, corresponding z -score is 1 .645.
01:14
So that would be, we reject if the z -score is greater than 1 .645 or less than negative 1 .645.
01:24
So to calculate, or actually, getting ahead of myself here, we need to make sure that we do satisfy the requirements for the standard normal distribution to be applicable here.
01:34
So we need to check what n times p0 times 1 minus p0 is, where p0 is the null hypothesized proportion.
01:42
So we have our n value is 700, p0 was 0 .52, 1 minus p0 would be 0 .48...