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, $F _ { L }$ 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 $F _ { \alpha / 2 } \text { and } F _ { L }$
can be denoted $F _ { 1 - \alpha / 2 }$
Find the critical values $F _ { L } \text { and } F _ { R }$
for a two-tailed hypothesis test based on the following values: n₁=9, n₂ -7 , $\alpha = 0.05$

Question

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 _ { 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 } \text { and } F _ { L }

can be denoted

F _ { 1 - \alpha / 2 }

Find the critical values

F _ { L } \text { and } F _ { R }

for a two-tailed hypothesis test based on the following values: n₁=9, n₂ -7 ,

\alpha = 0.05

Quizplus · Accepted Answer

For a two-tailed hypothesis test with $\alpha = 0.05$, degrees of freedom for the numerator $df_1 = 9 - 1 = 8$ and for the denominator $df_2 = 7 - 1 = 6$. Looking up the critical value for $F_{\alpha/2}$ for $df_1 = 8$ and $df_2 = 6$ gives $F_R = 5.5996$. To find $F_L$, interchange the degrees of freedom (making it $df_1 = 6$ and $df_2 = 8$) and take the reciprocal of the critical value found for these degrees of freedom, which gives $F_L = 0.2150$.

When Performing a Hypothesis Test for the Ratio of Two FRF _ { R }FR​

When Performing a Hypothesis Test for the Ratio of Two $F _ { R }$