What Are the Rejection Regions for Each of the Following $\sigma _ { 1 } / \sigma _ { 2 } ^ { 2 } = 1$

Essay

What are the rejection regions for each of the following sets of hypotheses? $\sigma _ { 1 } / \sigma _ { 2 } ^ { 2 } = 1$
$H _ { A } : \sigma _ { 1 } / \sigma _ { 2 } { } ^ { 2 } \neq 1$
$\mathrm { n } _ { 1 } = 9 \quad \mathrm { n } _ { 2 } = 20 \quad \alpha = 0.05$

b. $\quad \mathrm { H_0 } : \sigma _ { 1 } 2 / \sigma _ { 2 } { } ^ { 2 } = 1$
$\mathrm { H } _ { \mathrm {A } } : \sigma _ { 1 } { } ^ { 2 } / \sigma _ { 2 } { } ^ { 2 } < 1$
$\mathrm { n } _ { 1 } = 40 \quad \mathrm { n } _ { 2 } = 50 \quad \alpha = 0.10$

c. $\quad \mathrm { Ho } : \sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 } = 1$
$\mathrm { H } _ { \mathrm { A} } : \sigma _ { 1 } 2 / \sigma _ { 2 } ^ { 2 } > 1$
$\begin{array} { l l l } \mathrm { n } _ { 1 } = 10 & \mathrm { n } _ { 2 } = 8 & \alpha = 0.01\end{array}$