00:01
Okay, so we've got a question here about a hypothesis test.
00:04
We want to test whether people who listen to classical music have a different score on a test than the general population.
00:14
So the null hypothesis is going to be that the population score on this test among classical music listeners is equal to that of the rest of the population, which is 58.
00:25
And the alternative hypothesis is going to be that it's different to 58.
00:31
So that's actually part b.
00:33
Sorry, i haven't done this in order, but i've just sort of naturally done that to start with.
00:38
So then we can see that since this is a not equal to sign, it's a two -tailed test.
00:45
So that's the answer to part a.
00:47
Part c asks for the test statistic.
00:51
So the test statistic is given by the sample mean minus the population mean under the null hypothesis, which is 58, divided by the sample standard deviation over the square root of the sample size.
01:04
Now we've got all the samples there.
01:06
We know the sample size is 14, and we can compute the mean to be 51 .04, and we can compute the standard deviation to be 20 .81, those two decimal places each.
01:17
And this gives us a t -test statistic of minus 1 .25 to two decimal places.
01:24
Part d then asks for the critical t -value.
01:26
So we've got a two -sided test, so we're going to have two critical t -values, and they're going to be.....