0:00
Okay.
00:02
Let's say we have an official at a state department who claims that the proportion of 16 -year -old girls who are unwed mothers in his county, in his state, has gone below 20%.
00:48
Okay.
00:50
And so a random sample of girls in this age group were selected of 200 girls.
01:15
And we want to, and 35 are unwed mothers.
01:27
Okay.
01:29
And so we want to run a hypothesis test on this.
01:32
And to see if his claim is actually true or not.
01:38
And so the null is that the proportion, and we're going to let that be p, okay, that the true proportion of girls in his state of 16 years old, who are unwomened mothers, are actually equal to 0 .20%.
02:01
The alternative is that we're going to be the claim that is actually below that 20%.
02:10
Okay.
02:11
And so we know that p hat, that sample proportion, is actually going to be 35 out of 200, which is equal to 0 .175.
02:24
Okay.
02:26
So we know that to calculate the z statistic for this claim, it is our sample proportion minus our null divided by the square root of our sample proportion times one minus our sample proportion over our sample size.
02:47
And so this is going to be 0 .175 minus 0 .20.
02:54
And we can divide that.
02:56
By the 0 .175 times 1 minus 0 .175 and then divide by 200.
03:07
And when we do that, we get a negative 0 .884.
03:13
Okay.
03:14
And so we are told that a type 1 error is equal to 0 .05...