00:01
So in part a, we believe that the proportion with who had flu is 24%.
00:06
So we want to know how big of a sample size do we need for a 95 % confidence interval for the true proportion to have that margin of air be within 2 % or that needs to be our margin of air.
00:22
And so we know that the margin of air is to take the 1 .96, the z value, because our confidence interval looks like this.
00:30
This p hat, one minus p hat, and then over the sample size.
00:37
And this is our margin of error.
00:39
And so we use 1 .96 for 95%.
00:42
We will assume that that value is close to 0 .24.
00:46
And remember we use 0 .5 if we have no idea.
00:49
And so this 0 .76 is our complement, and we don't know what n is.
00:53
And we want that to be no more than 2%.
00:56
So doing our algebra, we end up having 1 .96.
01:00
Times the square root of 0 .24 times .76 divided by that .02.
01:08
And then if we square both sides, square that side and that square root cancels out, this becomes squared, this becomes squared, and then that square root will actually go away...