## Elementary Statistics (12th Edition)

Published by Pearson

# Chapter 7 - Estimates and Sample Sizes - 7-2 Estimating a Population Proportion - Basic Skills and Concepts: 14

#### Answer

a)0.61 b)0.0442 c)0.61-0.0442=0.5658

#### Work Step by Step

a) The best point estimate is equal to the proportion of the sample (x) divided by the sample size: $\hat{p}=\frac{x}{n}=\frac{492}{806}=0.61.$ b)$E=z_{\frac{\alpha}{2}}\cdot \sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}=2.575\cdot \sqrt{\frac{0.61\cdot (1-0.61)}{806}}=0.0442.$ c) Confidence interval: \$\hat{p}-E

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