Two Independent Samples of Sizes M and N and Variances ${ S } _ { 1 } ^ { 2 } \text { and } S _ { 2 } ^ { 2 }$

Essay

Two independent samples of sizes m and n and variances ${ S } _ { 1 } ^ { 2 } \text { and } S _ { 2 } ^ { 2 }$ are selected at random from two normal distributions with variances $σ _ { 1 } ^ { 2 } \text { and } σ _ { 2 } ^ { 2 } \text {. }$ In testing $H _ { o } : σ _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 } \text { versus } H _ { o} : σ _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 } \text {, }$ where the test statistic value is $f = s _ { 1 } ^ { 2 } / s _ { 2 } ^ { 2 } ,$ the rejection region for a level .05 test is either $f \geq$$\underline{\quad\quad}$ or $f \leq$$\underline{\quad\quad}$