## Elementary Statistics (12th Edition)

Published by Pearson

# Chapter 7 - Estimates and Sample Sizes - 7-2 Estimating a Population Proportion - Basic Skills and Concepts - Page 338: 17

#### Answer

a)0.93 b)p is between 0.93-0.0162=0.9138 and 0.93+0.0162=0.9462. c)The method is effective.

#### Work Step by Step

a) The best point estimate is equal to the proportion of the sample (x) divided by the sample size: $\hat{p}=\frac{x}{n}=\frac{879}{947}=0.93.$ b)$E=z_{\frac{\alpha}{2}}\cdot \sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}=2.575\cdot \sqrt{\frac{0.93\cdot (1-0.93)}{947}}=0.0162.$ Hence, the confidence interval: E is between $\hat{p}-E$ and $\hat{p}+E$, hence p is between 0.93-0.0162=0.9138 and 0.93+0.0162=0.9462. c) The method is effective, because without the method, the proportion would be approximately 50%, whilst here, according to b), 50% is much lower than the lower bound of the confidence interval.

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