00:01
So we know that we want to do the hypothesis test, and we're going to assume that the proportion at this person's school is equal to what the national average is, the point four, and alternately that the proportion at this girl's school is less than point four.
00:17
And picture -wise, it's like we're going to assume that the sampling distribution is centered around point four.
00:26
That's what we're going to assume.
00:27
Now she took a sample, a random sample, so that's good.
00:32
Oh, and let me find my number here.
00:35
Looks like she took a sample of size 361, and she found that the number of people who said that they were scared of public speaking was 135.
00:50
And we want to know, do we have evidence to say that her school is lower? so, well, let's find what that p hat is.
01:00
Is her p hat is 135 out of 361 and i'm just going to plug that in my calculator and i'm going to store it 135 divided by 361 so her proportion comes out to be 0 .37 roughly 4 and i'm going to store that in my value in my calculator as x now we want to know what's the likelihood that she gets a p hat that is less than or equal to a hundred 35 over 361 if the true proportion is 0 .4.
01:36
So we're getting something down here.
01:38
I'll just kind of plop it here.
01:40
And that area is our p value.
01:42
So we need to convert it to our test statistic, which is a z value.
01:48
And that means we need to take what we got minus what we're assuming and then divided by the standard deviation of this sampling distribution.
01:59
And we use 0 .4, 1 minus 0 .4 .1 .5.
02:02
4 divided by n which is the sample size of 361 and let's find out what that test statistic is and so i have left parentheses and i have that answer minus my point four and then in my parentheses for my numerator divided by the square root of 0 .4 times 0 .6 divided by that 361 and let's see what we get our test statistic comes out to be negative 1 .0098 -7, etc...