Specify the appropriate rejection region for testing $\mathrm { H } _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ in the given situation.
-$\mathrm { H } _ { \mathrm { a } } : \sigma _ { 1 } ^ { 2 } \sigma _ { 2 } ^ { 2 } ; \alpha = 0.01 , \mathrm { n } _ { 1 } = 10 , \mathrm { n } _ { 2 } = 21$

A) $F 3.46$
B) $| F | 3.46$
C) $\mathrm { F } 4.81$
D) $\mathrm { F } 2.84$

Question

Specify the appropriate rejection region for testing $\mathrm { H } _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ in the given situation.
-$\mathrm { H } _ { \mathrm { a } } : \sigma _ { 1 } ^ { 2 } > \sigma _ { 2 } ^ { 2 } ; \alpha = 0.01 , \mathrm { n } _ { 1 } = 10 , \mathrm { n } _ { 2 } = 21$

A) $F > 3.46$
B) $| F | > 3.46$
C) $\mathrm { F } > 4.81$
D) $\mathrm { F } > 2.84$

Quizplus · Accepted Answer

The rejection region for a right-tailed test of equality of variances is $F > F_{\alpha, n_1-1, n_2-1}$. For $\alpha = 0.01, n_1 = 10, n_2 = 21$, we have $F_{0.01, 9, 20} = 3.46$. Therefore, the rejection region is $F > 3.46$.

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 $\mathrm { H } _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$