00:01
First of all, we have 120 patients.
00:04
So that means that we can use a z test here.
00:09
So let's start by coming up with our null hypothesis and our alternative hypothesis.
00:25
So the null hypothesis, we're going to make that.
00:28
Let's see what we're trying to check, claim that the percent of insured patients is less than the expected percentage.
00:35
So we're going to say that the mean is equal to 0 .57, that on average, 57 % of treated patients are insured.
00:51
And then the alternative hypothesis is going to be that the mean is less than 0 .57, because that's what we're trying to test here.
01:00
So the first thing that we need to do is we need to come up with our z.
01:05
And z is equal to x whatever we're testing minus the mean divided by the standard deviation so the first thing that we need to do is get our mean in our standard deviation and so from our sample the sample mean is going to be just n times p so if 60 are insured a 60 out of 120 that's 0 .5 so the mean for our sample here is 0 .5.
01:46
And our standard deviation is going to be the square root of p times 1 minus p over n.
02:06
So we have the square root of in our proportion here is 0 .5 times 1 minus 0 .5, which is also just 0 .5 over n, which is 120.
02:23
So let's go ahead and calculate that in the calculator.
02:26
So 0 .5 times 0 .5 divided by 120 and then square root of that is 0 .0456.
02:54
All right.
02:55
Now what we're going to do is we're going to plug this into our z formula.
02:59
So x is whatever we're testing.
03:01
So we're testing to see is it 57 % or not.
03:05
So 0 .57 minus 0 .5 over 0 .0456.
03:18
So this is going to give us our test statistic.
03:23
0 .57 minus 0 .5, divided by 0 .0456 is 1 .54.
03:32
And i rounded to the nearest 100th place because that's how far the chart goes to.
03:45
Okay, now we need to get our critical value.
03:48
And we're going to use that to help us make our decision.
03:51
So first of all, it's at the 0 .01 significance level...