Working off a fairly limited statistical understanding, so apologies in advance if this question is ludicrously basic. This has to have happened to other people who have successfully solved this issue, but searching for what I think are relevant terms is getting me things like "Karlin's Conjecture for Random Replacement Sampling Plans," and I'm starting to panic.
Attempting to contact 1000 people for a survey. Plan was to get a list of the target population, draw a random sample of 1000, then contact those people. Problem was that the original list contained people who weren't actually part of the population, so our random sample of 1000 only contained around 650 people we could actually contact. For time & budgetary reasons, filtering the entire original list so it only contains our target population is impossible.
How do we fix this? One option is to take a second random sample of 1000, filter for the people who actually are in our target population, then contact everyone who fits the bill (guessing around 1300 total from both samples?).
Another option is to take a second random sample of 1000, filter for the people who actually are in our target population, take the resulting list of 1300 and randomly contact 1000 of them.
A third option is to throw the original sample back in to the list, take a larger initial random sample (1500-2000 people?), and contact everyone from that sample who meets our criteria. For time and sanity reasons we'd like to avoid this if possible.
All of these feel somehow "off" to me, given my incredibly basic statistical education. So, gurus: what am I missing? Is there a fourth option that makes more sense? Will our results be statistically valid given any of the above approaches? And does this affect our analysis in any way?