Let X∼Binomial(n,p)X \sim Binomial(n, p)X∼Binomial(n,p). What is the variance of the sample proportion p^=X/n\hat{p} = X/np^=X/n?
p(1−p)p(1-p)p(1−p)
np(1−p)np(1-p)np(1−p)
p(1−p)/np(1-p)/np(1−p)/n
p(1−p)/n\sqrt{p(1-p)/n}p(1−p)/n