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I have 5 different options(a,b,c,d,e) out of which one is correct(c). What should be the sample size(the number of person i should ask to answer) so that i can get 80% confidence the correct answer(c) 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

2 Answers 2

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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