This function obtains the confidence interval for a proportion. It is vectorized, so the user can evaluate it using single values or a vector.
ci_p_wald(x, n, conf.level = 0.95)A matrix with the lower and upper limits.
The expression to obtain the confidence interval is given below:
\(\hat{p} - z_{\alpha/2} \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \leq p \leq \hat{p} + z_{\alpha/2} \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}\),
where \(\hat{p} = \frac{x}{n}\) is the sample proportion, \(x\) the number of observed successes in the sample with size \(n\). The value \(z_{\alpha/2}\) is the \(1-\alpha/2\) percentile of the standard normal distribution (e.g., \(z_{0.025} = 1.96\) for a 95% confidence interval).
ci_p.
ci_p_wald(x=15, n=50, conf.level=0.95)
#> [,1]
#> [1,] 0.1729798
#> [2,] 0.4270202