## Confidence Interval for Proportion

Let $X$ be the observed number of individuals possessing certain attributes (number of successes) in a random sample of size $n$ from a large population with population proportion $p$.

## Formula

$100(1-\alpha)$% confidence interval for population proportion is

`$\hat{p} - E \leq p \leq \hat{p} + E$`

where,

`$\hat{p}=\dfrac{X}{n}$`

is the observed proportion of successes,`$E = Z_{\alpha/2} \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$`

is the margin of error,`$1-\alpha$`

is the confidence coefficient,`$Z_{\alpha/2}$`

is the critical value of $Z$.