8.6 Para la varianza

\(H_{0}:\sigma ^{2}=\sigma_{0}^{2}\)

8.6.1 Si se conoce la media

\[ T=\frac{\sum_{i=1}^{n}(x_{i}-\mu )^{2}}{\sigma _{o}^{2}}\ \ \in \ \ \chi_{n}^{2} \]

8.6.2 Si no se conoce la media

\[T=\frac{nS_{n}^{2}}{\sigma _{o}^{2}} = \frac{(n-1) \hat{S}_{n-1}^{2}}{\sigma _{o}^{2}} = \frac{\sum_{i=1}^n (x_{i}- \bar{x})^2}{\sigma _{o}^{2}} \ \ \in \ \ \chi_{n-1}^{2}.\]