Chapter 8, Problem 48PS

According to a new study released by Infosys. a global leader in consulting, outsourcing, and technology, more than three-quarters $\left(77\%\right)$ of U.S. consumers say that banking on their mobile device is convenient. (Data extracted from “Infosys Survey Finds Mobile Banking Customers Love Base and Convenience. Yet Reliability and Security Concerns Remain." PR Newswire, 2012. bit.ly/Ip9RUF.)

a. If you conduct a follow-up study to estimate the population proportion of U.S. consumers who say that banking on their mobile device is convenient, would you use a $\pi$ of 0.77 or 0.50 in the sample size formula?

b. Using you answer in part (a), �nd the sample size necessary to estimate. with $95\%$ con�dence. the population proportion to within $\pm \mathrm{0.03.}$