Statistics Sample Size and Margin of Error in Proportions
The relationship between sample size and margin of error in statistical inference for proportions is governed by a power-law scaling where precision improves inversely with the square root of $n$. Formally, under conditions satisfying normal approximation ($np \ge 10$ and $n(1-p) \ge 10$), the width of the confidence interval scales proportionally to $\frac{z_{\alpha/2} \sqrt{\hat{p}(1-\hat{p})}}{\sqrt{n}}$. This principle establishes that reducing uncertainty by a factor of two requires quadrupling the sample size, reflecting fundamental limits in binomial estimation within frequentist statistics.
Statistics Sample Size and Margin of Error in Proportions
The relationship between sample size and margin of error in statistical inference for proportions is governed by a power-law scaling where precision improves inversely with the square root of $n$. Fo…