00:01
In this question, we have a random sample of 36 data pairs, right? the sample mean of the difference with 0 .8 and it was a standard deviation of 2.
00:11
And you ask you to test at the alpha equals 5 % significance level.
00:18
The claim that the population mean of the difference is different from 0.
00:23
So basically, you ask you to test the non -hypothesis that meal is, different from zero.
00:32
So my non -hypothesity would be mule equals zero and the alternative one, of course, the mu not equal to zero, right? so this is a two -sided test.
00:41
Now, the first question you ask is, is it appropriate to use the student t distribution? and the answer, of course, yes, because these samples are randomly selected, right? so you can use the t distribution.
00:56
And the degree freedom, of course, is the sample size, so it's six minus one, so the degree freedom is given by 36 minus 1, that's 35.
01:05
And then we have the hypothesis, which i already stated here.
01:12
And then see we need to compute the sample test statistic.
01:15
I'm going to call that t.
01:17
We're going to do a t test.
01:18
So we're going to, i'm going to call the test statistic tape.
01:22
And that's, of course, given by the sample mean that's 0 .8 and divided by the sample standard deviation, divided by the scler of sample size, which is 36.
01:32
So you'll find this to be actually 2 .4, right? so that's my test statistic.
01:40
Now you can, of course, find also the p value...