00:01
So we have two random samples from independent populations.
00:04
We have n1 equals 45, n2 is equal to 42, x bar 1 is 50 .5, x bar 2 is 73 .5.
00:18
Our standard deviations are 57 .2 and 10 .1.
00:25
And we want to find a 94 % confidence interval for the difference of means.
00:37
So for mu 1 minus mu 2, assuming equal population variance.
00:44
So sigma 1 is equal to sigma 2.
00:49
Well, in that case, we have to use, let's see here, equal variances.
01:00
We have to calculate a pooled standard deviation, which is equal to n1 minus 1 times s1 squared plus n2 minus 1 times s2 squared divided by n1 plus n2 minus 2.
01:18
And that is going to be 57 .2 quantity squared times 44 plus 73 .5 quantity squared times 41 divided by 45 plus 42 minus 2.
01:39
So that will be equal to 7 .2 quantity squared times 44 plus 73 .5 quantity squared times 41 equals divided by, in parentheses, 45 plus 42 minus 2 plus parentheses.
02:02
This is the variance squared.
02:04
So pooled variance is 4 ,299 .44.
02:11
And that means that our pooled standard deviation is the square root of that, which is equal to...