Question

an f - test with 5 degrees of freedom in the numerator and 25 degrees of freedom in the denominator produced a test statistic whose value was 2.90. the null and alternate hypotheses were $h_0: sigma_1=sigma_2$ versus $h_1:sigma_1 > sigma_2$. part 1 of 2 find the critical values $f_{0.001}$ and $f_{0.025}$ for $f_{5,25}$. the critical value $f_{0.001}$ for $f_{5,25}$ is 8.35. the critical value $f_{0.025}$ for $f_{5,25}$ is 3.08. part 2 of 2 do you reject $h_0$ at the $alpha = 0.001$ and the $alpha = 0.025$ level? we select $h_0$ at the $alpha = 0.001$ level. we select $h_0$ at the $alpha = 0.025$ level.

Explanation:

Step1: Recall F - distribution critical value table

We use F - distribution tables to find critical values. The degrees of freedom for the numerator ($df_1$) is 5 and for the denominator ($df_2$) is 25.

Step2: Find $f_{0.001}$

Looking up in the F - distribution table with $\alpha = 0.001$, $df_1=5$, and $df_2 = 25$, we find the critical value. The critical value $f_{0.001,5,25}=7.76$.

Step3: Find $f_{0.025}$

Looking up in the F - distribution table with $\alpha=0.025$, $df_1 = 5$, and $df_2=25$, we find the critical value. The critical value $f_{0.025,5,25}=3.13$.

Answer:

The critical value $f_{0.001}$ for $df_1 = 5$, $df_2=25$ is $7.76$. The critical value $f_{0.025}$ for $df_1 = 5$, $df_2 = 25$ is $3.13$.