Answer
$F_0\lt F_{1-α,n_1-1,n_2-1}$: null hypothesis is not rejected.
There is not enough evidence to conclude that $σ_1\gtσ_2$
Work Step by Step
- Standard deviation.
$H_0:~σ_1=σ_2$ versus $H_1:σ_1\gtσ_2$
$F_0=\frac{s_1^2}{s_2^2}=\frac{12^2}{10^2}=1.44$
$d.f_1=n_1-1=31-1=30$
$d.f_2=n_2-1=51-1=50$
Right-tailed test:
$F_{α,n_1-1,n_2-1}=F_{0.05,30,50}=1.69$
(According to table VIII, for $d.f._1=20$, $d.f._2=10$ and area in the right tail = 0.05)
Since $F_0\lt F_{α,n_1-1,n_2-1}$, we do not reject the null hypothesis.
