My question is about the validity of a certain technique that I have seen in my workplace. This concerns analysis of a dataset that I am getting from a third-party. The details aren't important to me, I am just interested in whether the technique being used is statistically valid.
So the third party is drawing a sample of customers from a database and using this sample to make conclusions about a total customer base. Assume that the sample is basically representative of the population across the relevant attributes. Straightforward.
However, what if we want to know about a subset of this population? For various reasons, it isn't possible to take a sample for this subset. What do we do?
My first question is whether we can use the original sample to draw conclusions about the subset? Is this valid? My understanding is that you can only do this if your sample is also representative of the subset. Is that correct?
What the third party is actually doing is taking an estimate for the total population and multiplying by the relative size of the subset. They are also issuing confidence intervals for these estimates (I am not sure exactly how, my assumption is that they taking these from the total population). My second question is whether this is correct? Or does it depend on the dataset? If so, how? I understand this question is harder to know without details but my concern is really understanding whether this is a good idea or not in theory.