91Ó°ÊÓ

The numerator degrees of freedom is$v_1=7$

The denominator degrees of freedom is$v_2=9$

The alternative hypothesis is$H_a:{{\mathrm{σ}}_1}^2<{{\mathrm{σ}}_2}^2$

The level of significance is$\mathrm{Î\pm }=0.05$

As the alternative hypothesis is given to us, so we will set up a null hypothesis, that is$H_0:{{\mathrm{σ}}_1}^2={{\mathrm{σ}}_2}^2$

Using percentage points of the F-distribution$\mathrm{Î\pm }=0.05$, the critical value is 3.293.

Therefore, the rejection region is $F>3.293$.

The numerator degrees of freedom is V₁ =7

The denominator degrees of freedom is V₂ = 9

The alternative hypothesis is$H_a:{{\mathrm{σ}}_1}^2>{{\mathrm{σ}}_2}^2$

The level of significance is$\mathrm{Î\pm }=0.01$

As the alternative hypothesis is given to us, so we will set up a null hypothesis, that is$H_0:{{\mathrm{σ}}_1}^2={{\mathrm{σ}}_2}^2$

Using percentage points of the F-distribution$\mathrm{Î\pm }=0.01$, the critical value is

Therefore, the rejection region is $F>5.613$.

The numerator degrees of freedom is V₁ =7

The denominator degrees of freedom is V₂ = 9

The alternative hypothesis is$H_a:{{\mathrm{σ}}_1}^2≠{{\mathrm{σ}}_2}^2$

The level of significance is$\mathrm{Î\pm }=0.1$

As the alternative hypothesis is given to us, so we will set up a null hypothesis, that is$H_0:{{\mathrm{σ}}_1}^2={{\mathrm{σ}}_2}^2$

Using percentage points of the F-distribution$\mathrm{Î\pm }=0.1$, the critical value is

Therefore, the rejection region is 2,505.

The numerator degrees of freedom is V₁ =7

The denominator degrees of freedom is V₂ = 9

The alternative hypothesis is$H_a:{{\mathrm{σ}}_1}^2<{{\mathrm{σ}}_2}^2$

The level of significance is$\mathrm{Î\pm }=0.025$

As the alternative hypothesis is given to us, so we will set up a null hypothesis, that is $H_0:{{\mathrm{σ}}_1}^2={{\mathrm{σ}}_2}^2$

Using percentage points of the F-distribution $\mathrm{Î\pm }=0.025$, the critical value is 4.197

Therefore, the rejection region is $F>4.197$.