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: 15

Answer

a)0.43 b)0.0162 c)p is between 0.43-0.0162=0.4138 and 0.43+0.0162=0.4462. d)We are 90% sure that p is between 0.4138 and 0.4462.

Work Step by Step

a) The best point estimate is equal to the proportion of the sample (x) divided by the sample size: $\hat{p}=\frac{x}{n}=\frac{1083}{2518}=0.43.$ b)$E=z_{\frac{\alpha}{2}}\cdot \sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}=1.645\cdot \sqrt{\frac{0.43\cdot (1-0.43)}{2518}}=0.0162.$ c) Confidence interval: E is between $\hat{p}-E$ and $\hat{p}+E$, hence p is between 0.43-0.0162=0.4138 and 0.43+0.0162=0.4462. d)We are 90% sure that p is between 0.4138 and 0.4462.
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