Answer
$X_0^2\gt X_{1-α}^2$: null hypothesis is not rejected.
There is not enough evidence to conclude that the investment manager’s portfolio has less risk than the general market.
Work Step by Step
$H_0:~σ=18$ versus $H_1:~σ\lt18$
$X_0^2=\frac{(n-1)s^2}{σ_0^2}=\frac{(10-1)16^2}{18^2}=7.111$
Left-tailed test:
$n=10$
$d.f.=n-1=9$
$X_{1-α}^2=X_{0.95}^2=3.325$
(According to Table VII, for d.f. = 10 and area to the right of critical value = 0.95)
Since $X_0^2\gt X_{1-α}^2$, we do not reject the null hypothesis.
