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I have $5$ different options: ($a,b,c,d,e$) out of which one is correct ($c$ in this case).

What should be the sample size (the number of people I should ask to answer) so that I can get $80\%$ confidence that the correct answer is chosen?


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I think you've used the wrong tag. Distribution theory deals with distributions, not with confidence intervals. – Stijn May 3 '11 at 12:46

Without knowing something about the accuracy of the responses there is no answer. If your respondents are 100% accurate, one is enough. If they are random, no number is enough.

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More technically: without knowing the probability distribution associated with the population you're taking your samples from, the question is unanswerable as it stands – J. M. May 3 '11 at 12:48

If for each person you ask, there is a probability $p$ that they answer correctly, and if you consider the polled individuals' responses as independent then you can do the following calculation.

$P(\textrm{at least one is correct})$ = $1-P(\textrm{none is correct}) = 1-(1-p)^n$

for $n$ people asked. So if you want to be 80% certain at least one is correct, you should ask

$n \geq \frac{log(1-0.8)}{log(1-p)}$ people.


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