Suppose That You Wish to Estimate a Population Proportion and Want

Multiple Choice

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 of $0.3$ is used for $\hat { p }$ when determining the sample size. What values of the observed value of $\hat { p }$ will yield a larger margin of error than the one specified?

A) $0.3 < \hat { p } < 0.5$
B) $\hat { p } < 0.3$
C) $0.3 < \hat { p } < 0.7$
D) $\hat { p } > 0.3$