00:01
All right, so for the first problem here, we want to do a 99 % confidence interval for proportions.
00:06
We're told that the p -hat, which is a sample proportion, is 0 .47 or 47%, and this was out of 2 ,294 voters.
00:16
Okay, so to calculate a 99 % confidence interval for proportions, it's going to be p -hat plus or minus z -star times the square root of p -hat times 1 minus p -hat over n.
00:31
That z star comes from our 99 % confidence and so we just look up what the critical value is for 99 % confidence for a z star and that i'm just looking on my chart really quick is 2 .576 and then we know pha so we have all the pieces that we need here it's going to be 0 .47 plus or minus 2 .576 times the square root of 0 .47 times 1 minus 0 .47, which is 0 .53 divided by 2 ,294.
01:12
Okay, so let me compute that margin of error, 2 .576 times square root of 0 .47 times 0 .53 over 2 ,294, comes out to 0 .0 .0.
01:27
Let's see, we need 3 decimal places, so 0 .07.
01:33
0 .47 minus 0 .027 is 0 .43 for my low, and then for the high, 0 .47 plus 0 .027 is 0 .497.
01:48
So that's the answer to the first question...