Proportion Estimation
Proportion estimation is another common task for sample statistics.
We have sample proportion
where 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 y} is the number of subjects in the sample with a particular trait, and 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 n} is the sample size.
We have
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 \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 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 p}
