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 374: 5

Answer

a)543 b)247 c)543

Work Step by Step

a)$\alpha=1-0.98=0.02.$ Then, by using the table, the critical value: $z_{\alpha/2}=z_{0.01}=2.33.$ Hence the minimum sample size: $\frac{z_{\alpha/2}^2\cdot \sigma}{E^2}=\frac{2.33^2\cdot 0.25}{0.05^2}\approx543$. b)$\alpha=1-0.98=0.02.$ Using the table: $z_{\alpha/2}=z_{0.01}=2.33.$ Hence the minimum sample size:$\left (\frac{z_{\alpha/2}\cdot \sigma}{E}\right)^2=\left (\frac{2.33\cdot 337}{50}\right)^2\approx247$. c) We need to use the maximum out of a) and b), which is 543.
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.