00:01
We're looking at some sample data and we want to make a confidence interval.
00:04
We have the sample size n is 2540.
00:09
Sample proportion p -hat is 29 percent, 0 .29.
00:14
So the formula for a confidence interval for the population proportion is p -hat, our point estimate, plus and minus the margin of error, z root p -hat, 1 minus p -hat, over n.
00:29
So we have n, we have p -hat, we just need z.
00:33
We get that from a level of confidence.
00:36
So this is a binomial setup.
00:40
We have 2540 trials, probability p of success, p being the true percentage or true proportion rather.
00:49
We don't know what that is.
00:50
But we can make a normal approximation to the binomial and every possible sample you take, the sample proportion will fall somewhere along here.
01:02
So what we do is we put p -hat in the middle, we form an interval around it containing 99 percent of the area of this curve.
01:10
So we've been 99 percent confident this interval is long enough that it will contain p.
01:18
So that leaves one percent in the tables, so each tail is 0 .5 percent.
01:25
Z is the z -score to exclude these tables in the normal distribution...