The procedure used to evaluate the null hypothesis $\sigma_{1}=\sigma_{2}$ is the same as the procedure used to evaluate the null hypothesis $\sigma=\sigma_{0}$ where $\sigma_{0}$ is a constant.

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The procedure to evaluate the null hypothesis $\sigma_{1}=\sigma_{2}$ involves comparing two sample variances to test if two populations have equal variances, often using an F-test or Levene's test. In contrast, evaluating $\sigma=\sigma_{0}$ involves testing if a single population variance equals a specific value, typically using a chi-square test. These are fundamentally different statistical procedures.

The Procedure Used to Evaluate the Null Hypothesis σ1=σ2\sigma_{1}=\sigma_{2}σ1​=σ2​ Is the Same as the Procedure Used to Evaluate the the Same

The Procedure Used to Evaluate the Null Hypothesis $\sigma_{1}=\sigma_{2}$ Is the Same as the Procedure Used to Evaluate the the Same