Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 7 - Estimates and Sample Sizes - 7-2 Estimating a Population Proportion - Beyond the Basics: 43

Answer

p is more than 0.85-0.019=0.831 or less than 0.85+0.019=0.869.

Work Step by Step

E=0.022, $\hat{p}=0.85$. Hence $E_{1}=\frac{z_{\alpha}}{z_{\frac{\alpha}{2}}}\cdot E=\frac{1.645}{1.96}\cdot 0.22=0.019.$ Hence, the confidence interval: p is more than $\hat{p}-E$ or less than $\hat{p}+E$, hence p is more than 0.85-0.019=0.831 or less than 0.85+0.019=0.869.
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