00:01
All right, so we're looking at smoking and copd.
00:04
And we're testing the null hypothesis that concentration for nitrate for smokers and non -smokers are the same versus one -sided alternative.
00:15
So here's h -not, the null that they are the same.
00:18
Here's the one -side alternative, the alternate, that one is less than the other.
00:23
And here's the statistics we have.
00:27
And we're told to assume the population variances are the same, which is nice.
00:31
So this is telling us what test you use.
00:42
And this tells us it's going to be a two -sample t -test.
00:57
T -test because we have a small number of samples, as people being volunteering for the study.
01:11
So here we go.
01:12
We have the sample mean for the non -smokers and smokers as given here.
01:17
You pull that from the data here.
01:19
There's x bar 1, x bar 2.
01:23
Boom.
01:25
Sample, same deviation of one, sample standard deviation of two.
01:29
Sample size of 9 -11, 9 -1 -1 -lifelong non -smoking healthy volunteers, and 11 healthy volunteers.
01:37
Boom, 9 -11.
01:41
Now we are going to run our test, and we need to...
01:47
The formula for the test is the following.
01:56
Right, so it is the formula.
02:06
X bar 1 minus x bar 2.
02:08
So the pooled variance times 1 over n1.
02:17
So x bar 1, x bar 1, x bar 2 are given here.
02:21
So it's 16, 1, 5, 6 minus 2, 4, 6, 7, 2 is less than.
02:32
So we need this pooled variance bit, and we'll get that in just a second, but we have 1 over n.
02:36
Let's put in what we have.
02:39
Okay, so now we just need the pooled variance.
02:42
And that is given with this, formula n1 minus 1 times the sample variance of 1 plus n2 minus 1 times the sample variance of variance over n1 plus n2 minus 2 so that's the pool of variance and so we substitute what we have here n minus 1 is 8 so 8 we have the standard deviations for each of these so we square them to get the variance.
03:17
So 7 .029 squared plus, let's see, 11 minus 1 is going to be 10 times 7 ,534 squared all over.
03:34
9 plus 11 minus 2, so it's going to be 18.
03:39
Actually, i'll show the substitution.
03:41
It's good to see it.
03:42
9 plus 11 plus 2.
03:44
And that's the pool of variance.
03:46
And that's what this number is here.
03:48
This is a large number.
03:51
Look there.
03:53
So you substitute that right here.
03:55
So it's a big number.
03:57
So i'm just going to...
04:02
I'll put it in.
04:02
I'll put it in.
04:04
5 .3.
04:06
I'm going to erase this, which is fine...