Extending the Margin of Error Formula
A research organization uses the formula for the margin of error given by \(E = z_{\alpha/2}\sqrt{\frac{p(1-p)}{n}}\) to construct a confidence interval for a population proportion. Explain qualitatively how increasing the sample size \(n\) affects the margin of error \(E\). Then, assuming a worst-case scenario where \(p = 0.5\) (which maximizes variability) and a fixed critical […]