00:01
We have been given some sample data.
00:02
We want to use it to test sarah's claim.
00:05
So sarah's belief is that students sleep at least six hours per night.
00:10
So part one is to put the null and alternative hypotheses.
00:15
So sarah believes at least six.
00:18
So population mean would be at least six.
00:21
The other hypothesis, whoops, mu, would be it is less than six.
00:25
So those are the hypotheses.
00:27
I know which is which because the null hypothesis always gets an equal sign.
00:31
So that gets sarah's claim of at least.
00:33
It has the whole equals in there.
00:36
Ok, part two.
00:37
State the sample information.
00:41
So our sample size is 10.
00:43
We have 10 people.
00:44
The sample mean is calculated by taking each value, adding them up and dividing by the total.
00:50
So if i do that, if i add these up, i get 63 .1, giving us a mean of 6 .31.
00:59
And stating the sample standard deviation, that is not a nice thing to ask of you, because one, it's busy work, and two, you don't need it.
01:08
They have given you the population standard deviation.
01:12
But let's go ahead and do what they want.
01:14
We take each value, we subtract the sample mean, square it, sum the squares, divide by n minus 1, and we square root that.
01:24
So feel free to just feed this information into your calculator, make your calculator do it, or you can use software.
01:31
It's 1 .208 to three decimal places.
01:35
But i put that in red because we're not going to be using that.
01:38
We have the population standard deviation.
01:40
Why would we need to estimate it using a sample standard deviation? which brings us on to part three.
01:47
Okay, the test statistic.
01:48
So you have two options here.
01:50
It could be called z, it could be called t.
01:53
Z is if you know the population standard deviation, t is if you don't.
01:58
As it says plural, i suppose we'll calculate both, but we'll be using z.
02:02
Because z is preferable.
02:04
Basically, it's the z score of this sample mean...