00:02
For this question, we consider a sample of 15 private colleges whose mean tuition was $36 ,700, with a standard deviation of $6 ,500.
00:15
And we want to test whether the mean tuition for private colleges is different from 33 ,300.
00:24
And we are asked to choose our own significance level, so i'm going to choose a significance level of 0 .05.
00:30
The common significance levels for hypothesis testing are 0 .01, 0 .05.
00:35
And point one.
00:38
Now we're given the sample standard deviation and we're also told that the population is normal or approximately normal.
00:47
For part a we're asked to state the null and alternative hypotheses.
00:52
The null hypothesis is that the mean tuition for the private colleges is indeed 33 ,300 and the alternative is that it is different from 33 ,300.
01:07
So the claim that we are testing is the alternative, that the mean is different from 33 ,300.
01:17
Now we're also asked to draw the normal curve and mark the critical value, critical and non -critical regions.
01:23
Now since we have the sample standard deviation but not the population standard deviation given to us in the question, we have to use the t distribution rather than the normal distribution, even though the population is normally distributed.
01:37
And this is the t distribution with n minus 1 or 4.
01:43
14 degrees of freedom.
01:46
So if we draw the curve for the t distribution, it looks a lot like the normal distribution.
01:50
It just has broader tails.
01:52
This is the t distribution with 14 degrees of freedom.
01:56
It also has a mean of zero, and it's symmetrical about the mean.
02:02
For a two -tail test, we know this is a two -tail test because the alternative hypothesis is not equal to hypothesis.
02:09
That indicates a two -tail test.
02:11
For a two -tail test, there are two critical values, t sub -alph over two, and minus t sub alpha over 2.
02:23
This convention means that there's an area of alpha over 2 in the tail beyond the critical value.
02:32
And the same thing in this direction...