I have a statistics question that I've been wrapping my brain around but I can't seem to come up with a good answer.
Let's say we have a population N. In N, there are 2 sub populations A and B. We know the percentages of the sub populations. So for example, A is 40% of N and B is 60% of N.
Now we're given a statistic of N. So for example, let's say we're asking the entire population N if they are male or female.
We get the following results:
Male - 70% Female - 30%
However, we don't know which of these people comes from which of these sub populations. All we know, is that globally 70% are male.
Now, it would seem to me that we would also expect that 70% of A and 70% of B are male. However, the question I'm struggling with is the variance. How do we calculate the variance of the percentage of subpopulation A responses that are male?