The Basic Practice of Statistics 7th Edition

Published by W. H. Freeman
ISBN 10: 146414253X
ISBN 13: 978-1-46414-253-6

Chapter 22 - Inference about a Population Proportion - Chapter 22 Exercises - Page 534: 22.31a

Answer

$0.1695$ to $0.2219$

Work Step by Step

$\hat{p}=\frac{171+2}{880+4}\approx0.1957$ The z-value belonging to the $95\%$ confidence interval according to the table is $z=1.96$, thus the confidence interval is: $\hat{p}\pm z\sqrt{\frac{p(1-p)}{n}}$, which here is: $0.1957\pm 1.96\sqrt{\frac{0.1957\cdot(1-0.1957)}{884}}=0.1957\pm0.0262$ Thus the interval is from $0.1695$ to $0.2219$
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