Dear Fellow Statisticians,
I am trying to solve 2 sampling statistics problems, and I would much appreciate your help. Any insights that you could offer would be most welcomed!
Please consider the following 2 questions as completely separate.
1) I am sampling without replacement, and the items have different probabilities of being sampled. How do I implement this? I am not looking a mathematical treatment of this problem; I am simply looking for a procedure to do this. (Hopefully, it's easily implementable in a statistical computing software.)
I've read 4 textbooks on sampling, and none discuss how to do it. I see multiple papers online, but most have highly mathematical descriptions of estimators for the population totals, and I don't see any that gave a straightforward algorithm.
2) I need to do a sample size calculation in an acceptance sampling scheme. In my hypergeometric distribution, I'm looking for defects. The trick is that I know the following:
- the true proportion of defects is close to zero
- if there are defects in the population, it has an upper bound of 0.0125
How can I incorporate these pieces of information (especially the second point)? I sense that I can reduce the sample size if I use this prior knowledge, but I struggle to figure out exactly how to do so.
Thanks in advance for all of your ideas!
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