00:01
All right, so in this question we have been given that we need to conduct a study.
00:10
We're conducting a study rather to see if the probability of a true negative on a test for a cancer is significantly different from 0 .13.
00:18
So for that purpose we've set up our hypothesis test.
00:21
We've been given that our significance level is 0 .005.
00:26
Then we take a sample of 665 and find that there are 111 successes in that.
00:34
So i've written down the formula for the sample proportion in this case, which is just x over n, 11 over 665 in this case.
00:47
So we got to note an important thing that we do not know the population standard deviation.
01:01
Popst, i've just written as population standard deviation.
01:07
So therefore we have to obtain different methods of sort of going about it.
01:13
Okay, so i'm going to actually call this p.
01:18
P is fine.
01:19
P is just fine for that i guess.
01:21
Okay, so for the first step we've been asked to calculate the test statistic.
01:25
I'm going to just i guess call that like z, the critical value of z.
01:39
Well let's just call it t for test statistic.
01:41
It's probably a little bit of a better option.
01:45
All right, so for this the formula is p hat minus p over square root of p times 1 minus p over n.
02:00
Okay, now you got to give me a couple minutes to sort of enter that on my calculator because i haven't pre -solved this question.
02:08
So let's see 0 .13 all divided by square root of 3 divided by the number of samples which is 665.
02:40
So let me see what answer i get for this.
02:45
It's 2 .83.
02:46
Let me check how many decimal places we would want that to.
02:50
Three decimal places.
02:51
Okay, brilliant...