Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 7 - Estimates and Sample Sizes - 7-4 Estimating a Population Standard Deviation or Variance - Basic Skills and Concepts: 6

Answer

df=19, $X_{L}^2=6.844$, $ X_{R}^2=38.582$, $\mu$ is between 0.0288 and 0.0685.

Work Step by Step

$\alpha=1-0.99=0.01.$ By using the table we can find the critical chi-square values with with $df=sample \ size-1=20-1=19$. $X_{L}^2= X_{0.995}^2=6.844$ $ X_{R}^2= X_{0.005}^2=38.582$ Hence the confidence interval:$\mu$ is between $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(19)\cdot 0.04111^2}{38.582}}=0.0288$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(19)\cdot 0.04111^2}{6.844}}=0.0685.$
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.