When solving for the sample size needed to compute a 95 percent confidence interval for a population proportion "p," having a given error bound "E," we choose a value of $\hat { p }$
that makes $\hat { p } ( 1 - \hat { p } )$
as small as reasonably possible.

Question

When solving for the sample size needed to compute a 95 percent confidence interval for a population proportion "p," having a given error bound "E," we choose a value of $\hat { p }$ 
that makes $\hat { p } ( 1 - \hat { p } )$ 
as small as reasonably possible.

Quizplus · Accepted Answer

When determining the sample size for a confidence interval for a population proportion, we choose $\hat{p}$ to be 0.5 because this maximizes $\hat{p}(1-\hat{p})$, leading to the largest sample size and ensuring the interval is sufficiently wide for any proportion.

When Solving for the Sample Size Needed to Compute a 95