Plus Four 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 $p$. The estimator of the population proportion of success based on plus four rule is $\hat{p}=\frac{X+2}{n+4}$.
Formula
$100(1-\alpha)$% plus four confidence interval for population proportion is
$\hat{p} - E \leq p \leq \hat{p} + E$
where,
$\hat{p}=\dfrac{X+2}{n+4}$is the estimate of population proportion based on plus four rule,$E = Z_{\alpha/2} \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n+4}}$is the margin of error,$1-\alpha$is the confidence coefficient,$Z_{\alpha/2}$is the critical value of $Z$.
