I have a hypergeometric distribution with:(adsbygoogle = window.adsbygoogle || []).push({});

N=total population of red and green balls, I now this

K=total number of red balls, I don't know this

n=sample size (number of investigated balls), I can choose this

k=number of investigated balls that are red, I don't know this

Red balls are a problem and I want to make sure, with a certainty c, that in the total population the fraction K/N of red balls is lower that a certain value, called p_max.

How big must n be? And for a given n; what is the maximum value of k in order to approve the total population N. (I mean if I cannot guarantee with certainty c that K/N is below p_max I have to scrap the entire population N.)

For example, N=1000, c=0.95, and p=0.1.

I hope this is graduate level, at least it beats me :-)

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# A Sample size required in hypergeometric test

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