Answer
$X_0^2\gt X_α^2$: null hypothesis is rejected.
There is enough evidence to conclude that the birth weights of preterm babies have more variability than the birth weights of full-term babies.
Work Step by Step
$H_0:~σ=505.6$ versus $H_1:~σ\gt505.6$
$X_0^2=\frac{(n-1)s^2}{σ_0^2}=\frac{(41-1)840^2}{505.6^2}=110.409$
Right-tailed test:
$n=41$
$d.f.=n-1=40$
$X_α^2=X_{0.01}^2=63.691$
(According to Table VII, for d.f. = 40 and area to the right of critical value = 0.01)
Since $X_0^2\gt X_α^2$, we reject the null hypothesis.
