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 - Basic Skills and Concepts: 13

Answer

a)0.53 b)0.0309 c)0.53-0.0309=0.4991

Work Step by Step

a) The best point estimate is equal to the proportion of the sample (x) divided by the sample size: $\hat{p}=\frac{x}{n}=\frac{531}{1002}=0.53.$ b)$E=z_{\frac{\alpha}{2}}\cdot \sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}=1.96\cdot \sqrt{\frac{0.53\cdot (1-0.53)}{1002}}=0.0309.$ c) Confidence interval: $\hat{p}-E$

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