What hypothesis test?

I have a population of Z items, where X must pass and Y must fail. The thing is that the X that pass is not just a count (i.e. if 2 must pass, it has to be items A and B. It can't be C and D.) How do I figure out the sample size/what test should I use to test this? Also, how would I test it? Just have a sample size of items to fail? It needs to be risk-based, so ensuring all the failing items will fail with 90% confidence.

This may be super easy, but I can't seem to get my head around it having specific pass/fail items rather than just a 1 proportion test.



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Can you try to rewrite your question or put it into the actual context. I could not follow the A, B, C, and D component.
I have X items that are supposed to pass and Y that must fail. The population is huge, so I'm trying to find a sample size to test that is statistically significant to prove that all items that are supposed to fail actually do fail. The thing is that it is not just a count or proportion. So I can't say that 60% of the population fails, because it could be the items that aren't supposed to fail that have failed.

Does that make any more sense?
So are you implying that you know before hand which items in the population should fail, and which ones should not fail? your answer seems to imply you do.

So are you saying "I know items 1-10 SHOULD fail, however it's possible they don't". Same thing for successes?

If so I thnk you have two independent populations with two independent tests. Do a hypergeometric test (or binomial, poisson, etc..) which can be summarized pretty well based upon attribute sampling, with a tolerable threshold of 'failure' of say 1% (you're okay with up to 1% 'failure' on successes and 1% success on 'failures'. This number can obviously be adjusted as you see fit). Then perform your test according to attribute sampling on both populations.

Let me know if this makes sense