00:02
For question seven with this categorical data, our margin of error is found by using this part of the confidence interval formula.
00:09
So in this case, we want our margin of error to be 3 % or 0 .03.
00:15
So moe will be 0 .03.
00:18
At 95 % or 90 % confidence, the critical value z is 1 .645.
00:27
And then our sample proportion p hat is 4 % or 0 .04.
00:34
So i'll plug those in.
00:35
And the only thing we don't know is n.
00:38
So we're going to use some algebra to find n.
00:41
The first thing i'm going to do is divide both sides of this equation by 1 .645.
00:49
And 0 .03 divided by 1 .645 makes 0 .01823, and that equals the square root of in our numerator 0 .04 times 1 minus 0 .04 is 0 .034.
01:11
And then our denominator is n.
01:14
So now we need to get rid of the square root on the right by squaring both sides.
01:19
And the decimal on the left, when we square that, becomes a very small number...