Identify the rejection region that should be used to test $H _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ against $H _ { \mathrm { a } } : \sigma _ { 1 } ^ { 2 } \sigma _ { 2 } ^ { 2 }$ for $v _ { 1 } = 10 , v _ { 2 } = 29$, and $\alpha = .10$.
A) $F 1.83$
B) $F 2.53$
C) $F 3.00$
D) $F 2.18$

Question

Identify the rejection region that should be used to test $H _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ against $H _ { \mathrm { a } } : \sigma _ { 1 } ^ { 2 } > \sigma _ { 2 } ^ { 2 }$ for $v _ { 1 } = 10 , v _ { 2 } = 29$, and $\alpha = .10$.
A) $F > 1.83$
B) $F > 2.53$
C) $F > 3.00$
D) $F > 2.18$

Quizplus · Accepted Answer

The rejection region for a right-tailed F-test, where $H_a: \sigma_1^2 > \sigma_2^2$, is determined by the critical value of F at a given significance level $\alpha$. For $v_1 = 10$ and $v_2 = 29$ with $\alpha = .10$, the critical value from F-distribution tables is $F > 1.83$.

Identify the Rejection Region That Should Be Used to Test H0:σ12=σ22H _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }H0​:σ12​=σ22​

Identify the Rejection Region That Should Be Used to Test $H _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$