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 - Page 373: 1


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.
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.