Chapter 7, Problem 107CRE

Sample Size Formula (Part 1) From Formula 7.2, an estimate for margin of error for a $95\%$ confidence interval is $m=2\sqrt{\frac{\hat{p}\left(1-\hat{p}\right)}{n}}$ where $n$ is the required sample size and $\hat{p}$ is the sample proportion. Since we do not know a value for $\hat{p}$, we use a conservative estimate of $0.50$ for $\hat{p}$. Replace $\hat{p}$ with $0.50$ in the formula and simplify.