Answer
$F_0\gt F_{\frac{α}{2},n_1-1,n_2-1}$: null hypothesis is rejected.
There is enough evidence to conclude that the risk of the value funds and the risk of the growth funds differ.
Work Step by Step
$σ_1,s_1,n_1~and~d.f._1$ refer to value funds and $σ_2,s_2,n_2~and~d.f._2$ refer to growth funds.
$H_0:~σ_1=σ_2$ versus $H_1:σ_1\neσ_2$
$s_1=\sqrt {\frac{∑(x_{1_i}-x ̅_1)^2}{n_1-1}}=2.295$
$s_2=\sqrt {\frac{∑(x_{2_i}-x ̅_2)^2}{n_2-1}}=0.726$
$F_0=\frac{s_1^2}{s_2^2}=\frac{2.295^2}{0.726^2}=9.99$
$d.f_1=n_1-1=10-1=9$
$d.f_2=n_2-1=10-1=9$
Two-tailed test:
$F_{\frac{α}{2},n_1-1,n_2-1}=F_{0.025,9,9}=4.03$
(According to table VIII, for $d.f._1=120$, the closest value to 259, $d.f._2=200$, the closest value to 268, and area in the right tail = 0.025)
$F_{1-\frac{α}{2},n_1-1,n_2-1}=F_{0.975,9,9}=\frac{1}{F_{0.025,9,9}}=\frac{1}{4.03}=0.25$
Since $F_0\gt F_{\frac{α}{2},n_1-1,n_2-1}$, we reject the null hypothesis.
