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stats question

Posted By: Timothy Chow
Date: Tuesday, 21 June 2011, at 2:36 p.m.

In Response To: stats question (Christian Munk-Christensen)

I don't think your question has a definitive answer as stated because there are some hidden assumptions that need to be made, but here's an attempt to address what I think is your intended question.

It should be intuitively clear that the situation that is most likely to fool you is the case of exactly one piece that is not O.K. If there is exactly one piece that is not O.K., then the probability that you will miss it in 30 attempts is roughly (1 - 1/1400)^30 (this is sampling with replacement, and you're presumably sampling without replacement, but I'm just trying to get a rough estimate). I'm too lazy to go work this number out exactly, but by the binomial theorem, it should be close to 1 - 30/1400 or 98%. In other words you have only about a 2% chance of detecting that single bad piece with only 30 samples. Not at all confident.

Caveat: In most real-life scenarios, you will have some prior information about how likely there is to be a bad piece. That will change the answer. For example, if bad pieces have a systematic cause, so that almost certainly there will either be no bad pieces or a lot of bad pieces, then the situation is much more favorable for you. The aforementioned 2% "confidence" is a worst-case scenario.

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