For small samples, the margin of error is less than the standard error of $\hat { p }$

Question

Quizplus · Accepted Answer

The standard error of $\hat{p}$ measures the variability of the sample proportion $\hat{p}$ around the true population proportion $p$. The margin of error accounts for the uncertainty in estimating $p$ from $\hat{p}$, and is calculated as the product of the standard error and a critical value (typically a z-score). For small samples, both the standard error and the critical value increase, leading to a larger margin of error. Therefore, in general, the margin of error is greater than or equal to the standard error of $\hat{p}$.

For Small Samples, the Margin of Error Is Less Than p^\hat { p }p^​

For Small Samples, the Margin of Error Is Less Than $\hat { p }$