Essentials of Mathematical Probability and StatisticsA First Course For the Mathematically Inclined

Section 11.5 Hypothesis Test for one variance

$H_0 : \sigma^2 = \mu_0$ vs $H_a : \sigma^2 \neq \mu_0$

$H_0 : \sigma^2 = \sigma_0^2$ vs $H_a : \sigma^2 \gt \sigma_0^2$

$H_0 : \sigma^2 = \sigma_0^2$ vs $H_a : \sigma^2 \lt \sigma_0^2$