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: 1

Answer

a)50.99% b)p is between 46.84% and 55.14%. c)No.

Work Step by Step

a) The best point estimate is equal to the proportion of the sample (x) divided by the sample size: $\hat{p}=\frac{x}{n}=\frac{284}{557}=0.5099=50.99$%. b)$\alpha=1-0.95=0.05.$ $E=z_{\frac{\alpha}{2}}\cdot \sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}=1.95\cdot \sqrt{\frac{0.5099\cdot (1-0.5099)}{557}}=0.0415=4.15$% Hence the confidence interval:p is between 50.99%-4.15%=46.84% and 50.99%+4.15%=55.14%. c) The confidence interval counted in b) contains 50% and values lower than 50%, hence the answer is no.
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