When performing a hypothesis test for the ratio of two population variances, the upper critical $F$ value is denoted $F _ { R }$. The lower critical $F$ value, $F _ { \mathrm { L } }$, can be found as follows: interchange the degrees of freedom, and then take the reciprocal of the resulting $F$ value found in Table A-5. $F _ { R }$ can be denoted $F _ { \alpha / 2 }$ and $F _ { L }$ can be denoted $F _ { 1 - \alpha / 2 }$.
Find the critical values $F _ { L }$ and $F _ { R }$ for a two-tailed hypothesis test based on the following values: $n _ { 1 } = 25 , n _ { 2 } = 16 , \alpha = 0.10$
A) $0.7351,2.2378$
B) $0.5327,2.2878$
C) $0.4745,2.2878$
D) $0.4745,2.4371$

Question

Quizplus · Accepted Answer

The degrees of freedom are $df_1 = 24$ and $df_2 = 15$. For $\alpha = 0.10$, the critical values are found using an $F$ distribution table. $F_{R}$ is found directly for $df_1 = 24$, $df_2 = 15$, and $\alpha/2 = 0.05$, which is 2.2878. $F_{L}$ is the reciprocal of the $F$ value for $df_1 = 15$, $df_2 = 24$, and $\alpha/2 = 0.05$, which is 0.4745.

When Performing a Hypothesis Test for the Ratio of Two FFF

When Performing a Hypothesis Test for the Ratio of Two $F$