Chapter 10.9, Problem 81E

a.

To determine

Verify that the rejection region $\left\{F>F_{{\nu }_2,\frac{\alpha }{2}}^{{\nu }_1}\text{ or }F<{\left(F_{{\nu }_1,\frac{\alpha }{2}}^{{\nu }_2}\right)}^{-1}\right\}$ is the same as the rejection region $\left\{\frac{S_1^2}{S_2^2}>F_{{\nu }_2,\frac{\alpha }{2}}^{{\nu }_1}\text{ or }\frac{S_2^2}{S_1^2}>F_{{\nu }_1,\frac{\alpha }{2}}^{{\nu }_2}\right\}$.

b.

To determine

Show that $P\left(\frac{S_L^2}{S_S^2}>F_{{\nu }_S,\frac{\alpha }{2}}^{{\nu }_L}\right)=\alpha$ under $H_0$ using Part (a).