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: 19

Answer

a)0.5. b)0.44. c)p is between 0.44-0.0764=0.3636 and 0.44+0.0764=0.5164. d)The ability doesn't seem to be too good.

Work Step by Step

a) One choice is correct out of the two, so the expected proportion is: $p=\frac{1}{2}=0.5.$ b)The best point estimate is equal to the proportion of the sample (x) divided by the sample size: $\hat{p}=\frac{x}{n}=\frac{123}{280}=0.44.$ c)$E=z_{\frac{\alpha}{2}}\cdot \sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}=2.575\cdot \sqrt{\frac{0.44\cdot (1-0.44)}{280}}=0.0764.$ Hence, the confidence interval: E is between $\hat{p}-E$ and $\hat{p}+E$, hence p is between 0.44-0.0764=0.3636 and 0.44+0.0764=0.5164. d)The ability doesn't seem to be too good, because the expected proportion us in the confidence interval.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.