00:01
For this problem, the first thing that we're going to need to do is calculate our sample proportions.
00:05
P hat 1 will be r1 over n1, which, let's see here, that's going to be 23 over 85, giving a result of 0 .2706.
00:16
Then our second sample proportion, p hat 2, well that's r2 over n2, so that's going to be 31 over 96, for a result of 0 .3229.
00:32
And then we need our pooled proportion, p bar, which is r1 plus r2, divided by n1 plus n2.
00:47
So plugging in our values there, that's 23 plus 31, divided by 85 plus 96, oh let me turn that into a decimal, that's 0 .2983.
01:05
Now our confidence interval is going to be in the form of p hat 1 minus p hat 2, plus or minus a margin of error, which i'll write as e there, where e, the margin of error, will be a z -score for a tail proportion of, well let's see here, 91 % is going to be 1 minus alpha, so that means that our alpha has to be, or 1 minus alpha times 100%.
01:34
So that means that our alpha, the remainder, between 91 % and 100 % would be 0 .09, and we want a tail proportion for a z -score of half of alpha.
01:45
So we want a z -score with a tail proportion of 0 .045.
01:50
Then we multiply that by the square root of p bar times 1 minus p bar, times 1 over n1 plus 1 over n2.
02:07
So now i have, let's see here, i'll use a left tail table here for finding that critical z -score, but we really just care about the magnitude...