Answer
$X_0^2\gt X_{1-α}^2$: null hypothesis is not rejected.
There is not enough evidence to conclude that there is less variability in the filling machine.
Work Step by Step
$H_0:~σ=0.42$ versus $H_1:~σ\lt0.42$
$X_0^2=\frac{(n-1)s^2}{σ_0^2}=\frac{(19-1)0.38^2}{0.42^2}=14.735$
Left-tailed test:
$n=19$
$d.f.=n-1=18$
$X_{1-α}^2=X_{0.99}^2=7.015$
(According to Table VII, for d.f. = 18 and area to the right of critical value = 0.99)
Since $X_0^2\gt X_{1-α}^2$, we do not reject the null hypothesis.
