00:01
So here we're asked to find a 90 % confidence interval for the difference in proportions.
00:10
And we have for group 1, our early, or the readers, or the kids that were read to more than 3 times per week.
00:20
We have the number that read before age 4 is 53, and our n1 is 53 plus 40, so that is 93.
00:33
And our p proportion estimate then is 53 over 93.
00:39
And for group 2, the ones that were not read to as often, less than 3 times per week, we have x2.
00:49
The ones that started reading by age 4 is equal to 42.
00:55
And our n2 is 42 plus 35, which is 77.
01:01
So our p hat 2 is 42 over 77.
01:07
And then your alpha here is 10%, because we want a 90 % confidence interval.
01:16
So our confidence interval formula for p1 minus p2 is going to be p hat 1 minus p hat 2 plus or minus z alpha over 2, which is 0 .05, times the square root of p hat 1 times 1 minus p hat 1 over n1 plus p hat 2 times 1 minus p hat 2 over n2.
01:54
And this is going to be, let's see here, we have 53 over 93 minus 42 over 77 plus or minus the z score for 0 .05.
02:12
It's going to be 1 .645...