Answer
$X_0^2\lt X_{1-α}^2$: null hypothesis is rejected.
There is enough evidence to conclude that the standard deviation of heights of major-league baseball players is less than 2.9 inches.
Work Step by Step
$H_0:~σ=2.9$ versus $H_1:~σ\lt2.9$
$X_0^2=\frac{(n-1)s^2}{σ_0^2}=\frac{(20-1)2.059^2}{2.9^2}=9.5779$
Left-tailed test:
$n=20$
$d.f.=n-1=19$
$X_{1-α}^2=X_{0.90}^2=11.651$
(According to Table VII, for d.f. = 19 and area to the right of critical value = 0.90)
Since $X_0^2\lt X_{1-α}^2$, we reject the null hypothesis.
