Elementary Statistics (12th Edition)

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

Chapter 7 - Estimates and Sample Sizes - Review - Review Exercises - Page 374: 6


p is between 0.6152 and 0.6648.

Work Step by Step

The best point estimate is equal to the proportion of the sample (x) divided by the sample size: $\hat{p}=\frac{x}{n}=0.64.$ $\alpha=1-(confidence \ level)=1-0.9=0.1.$ According to the table: $z_{\alpha/2}=z_{0.05}=1.645.$ $E=z_{\frac{\alpha}{2}}\cdot \sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}=1.645\cdot \sqrt{\frac{0.64\cdot (1-0.64)}{1011}}=0.0248.$ Confidence interval: p is between 0.64-0.0248=0.6152 and 0.64+0.0248=0.6648.
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