Statistics: Informed Decisions Using Data (4th Edition)

Published by Pearson
ISBN 10: 0321757270
ISBN 13: 978-0-32175-727-2

Chapter 11 - Section 11.4 - Assess Your Understanding - Skill Building - Page 574: 9

Answer

$F_{1-\frac{α}{2},n_1-1,n_2-1}\lt F_0\lt F_{\frac{α}{2},n_1-1,n_2-1}$: null hypothesis is not rejected. There is not enough evidence to conclude that $σ_1\neσ_2$.

Work Step by Step

$F_0=\frac{s_1^2}{s_2^2}=\frac{3.2^2}{3.5^2}=0.84$ $d.f_1=n_1-1=16-1=15$ $d.f_2=n_2-1=16-1=15$ Two-tailed test: $F_{\frac{α}{2},n_1-1,n_2-1}=F_{0.025,15,15}=2.86$ (According to table VIII, for $d.f._1=15$, $d.f._2=15$ and area in the right tail = 0.025) $F_{1-\frac{α}{2},n_1-1,n_2-1}=F_{0.975,15,15}=\frac{1}{F_{0.025,15,15}}=\frac{1}{2.86}=0.35$ Since $F_{1-\frac{α}{2},n_1-1,n_2-1}\lt F_0\lt F_{\frac{α}{2},n_1-1,n_2-1}$, we do not reject the null hypothesis.
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.