00:01
We're looking at a competence interval for a population proportion based on a sample of 250 individuals.
00:08
So the sample size n is 250.
00:11
We want to know the multiplier that we're going to be using here for a 92 % confidence interval.
00:17
So what is the formula for a confidence interval for a population proportion? it's p -hat, the sample proportion, plus and minus the margin of error.
00:28
Z root p hat, 1 minus p hat over n.
00:35
So the multiplier that we're looking for here is z.
00:39
So the sample size doesn't actually come into z.
00:43
It comes into a margin of error, but not necessarily z.
00:48
So let's have a look.
00:51
Z is based on the normal distribution.
00:54
So if you have samples of size at least 30, your sample proportions are approximately normally distributed.
01:01
So if you make a normal distribution with p hat in the middle, this can represent your confidence interval.
01:07
Because all the other sample proportions, they're going to follow a normal curve.
01:12
And the population proportion is somewhere along here.
01:15
So i put down my interval, say, okay, 92 % of the area of this curve is in the interval...