Answer
$X_0^2\lt X_α^2$: null hypothesis is not rejected.
There is not enough evidence to conclude that the standard deviation of yield strength exceeds 7000 psi.
Work Step by Step
$H_0:~σ=7000$ versus $H_1:~σ\gt7000$
$X_0^2=\frac{(n-1)s^2}{σ_0^2}=\frac{(20-1)7500^2}{7000^2}=21.811$
Right-tailed test:
$n=20$
$d.f.=n-1=19$
$X_α^2=X_{0.01}^2=36.191$
(According to Table VII, for d.f. = 19 and area to the right of critical value = 0.01)
Since $X_0^2\lt X_α^2$, we do not reject the null hypothesis.
