Answer
$X_0^2\lt X_{1-α}^2$: null hypothesis is rejected.
There is enough evidence to conclude that the recalibration was effective.
Work Step by Step
$H_0:~σ=0.004$ versus $H_1:~σ\lt0.004$
$X_0^2=\frac{(n-1)s^2}{σ_0^2}=\frac{(25-1)0.0025^2}{0.004^2}=9.375$
Left-tailed test:
$n=25$
$d.f.=n-1=24$
$X_{1-α}^2=X_{0.99}^2=10.856$
(According to Table VII, for d.f. = 24 and area to the right of critical value = 0.99)
Since $X_0^2\lt X_{1-α}^2$, we reject the null hypothesis.
