Solve the Problem $\mathrm { F }$ Value Is Denoted $\mathrm { F } _ { \mathrm { R } }$

Multiple Choice

Solve the problem.
-When performing a hypothesis test for the ratio of two population variances, the upper critical $\mathrm { F }$ value is denoted $\mathrm { F } _ { \mathrm { R } }$ . The lower critical $\mathrm { F }$ value, $\mathrm { F } _ { \mathrm { L } }$ , can be found as follows: interchange the degrees of freedom, and then take the reciprocal of the resulting $\mathrm { F }$ value found in table $\mathrm { A } - 5$ . $\mathrm { F } _ { \mathrm { R } }$ can be denoted $\mathrm { F } _ { \alpha / 2 }$ and $\mathrm { F } _ { \mathrm { L } }$ can be denoted $\mathrm { F } _ { 1 - \alpha / 2 }$
Find the critical values $\mathrm { F } _ { \mathrm { L } }$ and $\mathrm { F } _ { \mathrm { R } }$ for a two-tailed hypothesis test based on the following values:
$$n _ { 1 } = 4 , n _ { 2 } = 8 , \alpha = 0.05$$

A) $0.1703,5.8898$
B) $0.1112,5.0453$
C) $0.0684,5.8898$
D) $0.1211,4.3541$