If X∼Binomial(n,p)X \sim \text{Binomial}(n, p)X∼Binomial(n,p), what is the variance of the sample proportion p^=X/n\hat{p} = X/np^=X/n?
np(1−p)np(1-p)np(1−p)
p(1−p)p(1-p)p(1−p)
p(1−p)n\frac{p(1-p)}{n}np(1−p)
p(1−p)n2\frac{p(1-p)}{n^2}n2p(1−p)