00:01
If our margin of error is 4%, it's gonna be 0 .04, and that's gonna be the standard deviation over square root of n.
00:13
Um, let's see, do we know how large is the population? we don't know the sample size, that's what we're trying to figure out.
00:20
We want to construct a 95 % confidence interval, so at 95%, z is gonna be 1 .96.
00:28
That's a known value, so the confidence interval is gonna be the mean.
00:33
Well, actually, sorry because we're talking about a proportion.
00:38
Um, it's gonna be p plus and minus z times standard deviation over square root of n.
00:54
Um, so our standard deviation when we're using p, so our margin of error s over square root of n, is gonna be square root of p times 1 minus p over n.
01:16
So we can just solve this way.
01:18
So this is gonna be equal to 0 .04.
01:22
So i'm going to, um, start by plugging in my first value of p equals 0 .3.
01:30
Then we're gonna have, um, square root of 0 .3 times 1 minus 0 .3, so 0 .7 over n, we don't know what that is, is equal to 0 .04.
01:45
And i'm gonna square both sides.
01:47
Also, i'm gonna multiply by 0 .3 by 0 .7.
01:53
So 0 .21 over n equals, and 0 .04 squared is 0 .0016...