Answer
$X_0^2\lt X_α^2$: the null hypothesis is not rejected.
There is not enough evidence to conclude that the population variance is greater than 10.
Work Step by Step
$H_0:~σ^2=10$ versus $H_1:~σ^2\gt10$
$X_0^2=\frac{(n-1)s^2}{σ_0^2}=\frac{(16-1)13.7}{10}=20.55$
Right-tailed test:
$n=16$
$d.f.=n-1=15$
$X_α^2=X_{0.05}^2=24.996$
(According to Table VII, for d.f. = 15 and area to the right of critical value = 0.05)
Since $X_0^2\lt X_α^2$, we do not reject the null hypothesis.
