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?
Thanks
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?
Thanks
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.
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.
Cheers