Suppose that you wish to estimate a population proportion and want to determine a sample size that will ensure a given margin of error for a $95 \%$ confidence interval. Suppose further that an educated guess is not available for $\hat { \mathrm { p } }$ and that $0.25$ is used for the value of $\hat { \mathrm { p } } ( 1 - \hat { \mathrm { p } } )$ when determining the sample size. True or false, if the observed value of $\hat { \mathrm { p } }$ is not equal to $0.5$, then the sample size will be larger than necessary?

Question

Quizplus · Accepted Answer

The Answer of Suppose that you wish to estimate a population proportion and want to determine a sample size that will ensure a given margin of error for a $95 \%$ confidence interval. Suppose further that an educated guess is not available for $\hat { \mathrm { p } }$ and that $0.25$ is used for the value of $\hat { \mathrm { p } } ( 1 - \hat { \mathrm { p } } )$ when determining the sample size. True or false, if the observed value of $\hat { \mathrm { p } }$ is not equal to $0.5$, then the sample size will be larger than necessary?

Suppose That You Wish to Estimate a Population Proportion and Want