Essentials of Statistics (5th Edition)

Published by Pearson
ISBN 10: 0-32192-459-2
ISBN 13: 978-0-32192-459-9

Chapter 7 - Estimates and Sample Sizes - 7-2 Estimating a Population Proportion: 22

Answer

p is between 14.2% and 27.4%.

Work Step by Step

The best point estimate is equal to the proportion of the sample (x) divided by the sample size: $\hat{p}=\frac{x}{n}=0.208.$ $E=z_{\frac{\alpha}{2}}\cdot \sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}=1.96\cdot \sqrt{\frac{0.208\cdot (1-0.208)}{144}}=0.066.$ Confidence interval: p is between 0.208-0.066=0.142=14.2% and 0.208+0.066=0.274=27.4%.
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