Proportion Estimation

Proportion estimation is another common task for sample statistics.

We have sample proportion

${\hat {p}}={\frac {y}{n}}$

where $y$ is the number of subjects in the sample with a particular trait, and $n$ is the sample size.

We have

$\mu _{\hat {p}}=p,\sigma _{\hat {p}}={\sqrt {\frac {p(1-p)}{n}}}$

and standard error

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle SE = \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}} }

Wilson-Adjusted CI for p

Correcting the sample proportion narrows the confidence interval. We do this with the Wilson-Adjusted estimate for $p$

${\widetilde {p}}$