Specify the appropriate rejection region for testing $\mathrm { H } _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ in the given situation.
- $\mathrm { H } _ { \mathrm { a } } : \sigma _ { 1 } ^ { 2 } < \sigma { } _ { 2 } ^ { 2 } ; \alpha = 0.05 , \mathrm { n } _ { 1 } = 21 , \mathrm { n } _ { 2 } = 8$

Question

Specify the appropriate rejection region for testing $\mathrm { H } _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ in the given situation.
-$\mathrm { H } _ { \mathrm { a } } : \sigma _ { 1 } ^ { 2 } < \sigma { } _ { 2 } ^ { 2 } ; \alpha = 0.05 , \mathrm { n } _ { 1 } = 21 , \mathrm { n } _ { 2 } = 8$
A) $F > 3.44$
B) $F > 3.01$
C) $F > 2.51$
D) $| F | > 2.51$

Quizplus · Accepted Answer

For a one-tailed test with $\mathrm { H } _ { \mathrm { a } } : \sigma _ { 1 } ^ { 2 } < \sigma { } _ { 2 } ^ { 2 }$, the rejection region is $F > F_{\alpha, n_2-1, n_1-1}$. With $\alpha = 0.05$, $n_1 = 21$, and $n_2 = 8$, the critical value is approximately 2.51.

Specify the Appropriate Rejection Region for Testing H0:σ12=σ22\mathrm { H } _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }H0​:σ12​=σ22​

Specify the Appropriate Rejection Region for Testing $\mathrm { H } _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$