00:01
In this question we're looking at box office revenues and they're in millions of dollars and we're looking at dramas and comedies and we're given an n, an x bar and an s for each of them.
00:28
So we're looking at 15 dramas and 13 comedies.
00:33
The dramas took a mean of 180 million versus 140 million for the comedies and the standard deviation of the sample was 60 for dramas and 20 for comedies.
00:49
So now what we're going to do is because these standard deviations are very different we can't assume that the underlying standard deviation is the same.
01:00
So what we want to do is work out a standard error and that's going to be the square root of s1 squared over n1 plus s2 squared over n2.
01:10
So that's the square root of 60 squared over 15 plus 20 squared over 13 which is 16 .4551.
01:25
We're looking for a confidence interval so let's just say we want a confidence interval for the difference in means at a confidence level of 99%.
01:45
So that's our confidence parameter.
01:53
Now because we have different standard errors we're going to need to work out our degrees of freedom using the saturth rate equation s1 squared over n1 plus s2 squared over n2 squared divided by s1 to the 4 over n1 squared n1 minus 1 plus s2 to the 4 over n2 squared n2 minus 1.
02:18
So in the numerator we have 60 squared over 15 plus 20 squared over 13 and we have to square that.
02:35
So i'm just going through and squaring that now.
02:40
Then in the denominator we have 60 to the 4 divided by 15 squared times 14 plus 20 to the 4 divided by 13 squared times 12 and that gives us 17 .4846 degrees of freedom...