00:01
We have the population proportion p equals 0 .31 and we're going to be taking two samples, size 13 and size 69.
00:12
In both cases we want the standard error.
00:17
Okay, so initially what we're looking at here is a binomial experiment.
00:26
We have some number of trials, 13 in part a, 69 in part b, and the probability of success on each trial is 0 .31.
00:35
The binomial variable is x, a probability distribution for the number of successes in the sample.
00:45
We're going to take a normal approximation to this.
00:48
We can't really for the smaller sample, but if we just pretend we do, the calculations will still work out.
01:02
The mean of this, mu, is np, and the standard deviation, sigma, is root np, 1 minus p.
01:08
See, this holds true regardless of the shape of the binomial.
01:11
It doesn't have to be symmetric for that to happen.
01:14
These are just the mean and standard deviation of the binomial distribution.
01:19
This distribution is still a probability distribution for x...