Answer to Question #204788 in Statistics and Probability for xsamdanielx

Question

If a researcher wants to estimate the proportion of customers of a coffee shop that favor the new brand of coffee the shop is serving to within 0.08 with probability 0.95, how many customers should they survey if the true proportion is assumed to be approximately 0.75 from previous studies?

Answer 1

$ME=z_{0.025}\sqrt{\frac{p(1-p)}{n}}.$

$n=({\frac{z_{0.025}}{ME}})^2p(1-p)=(\frac{1.96}{0.08})^20.75(1-0.25)=113.$