00:02
All right, so we're given some data on the burning times and minutes of chemical fliers of two different formulations.
00:12
And so we're interested in both the mean and variance of these burning times.
00:18
And the first thing we're going to do is test for equality of variances.
00:22
Are the variances of type 1 versus type 2 equal? and we're going to do this with an f test.
00:30
Oh, and we're told the test of the alpha of 0 .05.
00:34
And this is given as the sample variance of the larger one, whichever one it is, divided by the sample variance of the smaller one.
00:45
And then we're going to, let's state the hypotheses.
00:50
So we assume they're equal.
00:51
This is our, we assume equal.
00:55
So we're going to assume this.
01:16
We're going to assume equality.
01:18
The alternative hypothesis is that they're not equal.
01:23
And actually it's going to end up being a one -tail test.
01:25
It's going to be the variance of the, whatever one's larger is significantly larger.
01:36
All right.
01:37
So what we're going to do is calculate the standard deviations of each and then we're on our test.
01:43
So i use my spreadsheet to do this work for us.
01:47
And here's what we end up with.
01:50
I use the spreadsheet function called s t dv .s.
01:57
And you put in your data.
01:59
It out pops the sample standard deviation.
02:02
Just make sure you do with this sample because otherwise this population and that's not what we want.
02:08
It's because this is a sample.
02:09
So we find that type 2 is a larger.
02:12
So this is going to end up with type 2 here.
02:16
So let's change our hypothesis here.
02:24
Just so that we can be clear with our statistic here.
02:33
Now we put square the sample standard deviations.
02:36
We have the variance and we have these values.
02:40
And we end up with an f statistic.
02:41
Of 1 .022.
02:46
And i use a spreadsheet function called f dist.
02:52
And this gives us the p value that we're looking for.
02:55
We just have to put in the f statistic, which we have.
02:58
The degrees of freedom of the numerator, and the degrees of freedom in the denominator.
03:03
And they're both nine, because the degrees of freedom in this case are given as n minus one.
03:08
So 10 minus 1 is 9.
03:11
And doing that, we get a number of the number.
03:13
At a p value of 0 .0487.
03:18
So that means we fail to reject h0.
03:22
And we say that they're equal.
03:25
Right, so that means we're going to use that outcome to look at whether or not the means of these are equal.
03:34
So the assumption, the null hypothesis is at the mean of group one, sequence of the mean of group two.
03:44
The alternative hypothesis is that the mean of group one is not equal to the mean of group two.
03:53
So we're looking for not equal because the keyword is testing that they're equal.
04:03
So the counterpart to that would be not equal.
04:06
And for that we're going to use a t test.
04:08
Oh, and we're told the alpha is 0 .05 again.
04:12
So with this, we're going to use a t test for the difference of two means.
04:15
So we're going to get the mean of one minus the mean of the second.
04:19
And these are the sample means all over.
04:23
Now because the variance to equal, we can pool the variances, so we're going to get the pooled variance times one over the sample size of one plus one over the sample size of two.
04:34
So let's go ahead and do that.
04:36
So the sample variance is equal to the sample size of one minus one times the sample variance of one plus the sample variance of two, plus the sample variance of two, all over and one plus and two minus two.
04:55
So we have all this information.
04:58
We have the variances.
04:59
We have the sample sizes.
05:01
We plug everything in, and we end up with the pool of variance of 86 .77...