00:01
All right, so we have this researcher who wants to estimate with 95 % confidence, the population proportion, so we're doing a 95 % confidence interval for p.
00:16
Okay, and we want this estimate to be accurate within 2%.
00:24
So that means that 2 % means to be our margin of error.
00:32
So for a, when we have no preliminary information available, and we want to find the minimum sample size needed, well, to calculate a confidence interval for p, right, we have the following formula.
00:51
Okay, that's the formula for calculating it.
00:53
This part is the margin of error, right? so we want that part, the z star, times the square root of p hat times one minus p hat over n.
01:04
We want that to equal the margin of error.
01:08
Okay? so before i actually put any numbers in here, i'm just going to solve for n, and then i can put all the numbers in after.
01:15
So n is stuck under the square root right now.
01:18
So i'm going to get rid of this z, which was being multiplied by the square root, by dividing.
01:23
So that gives me the square root of p -hat times 1 minus p -hat over n should equal the margin of error divided by the z -star.
01:34
Next to get rid of the square root, i'm going to square both sides.
01:38
So i get p hat times 1 minus p hat over n should equal, in parentheses, the margin of error over the z star squared.
01:50
And then with a little bit of algebraic manipulation, i can actually just kind of swap these two...