Robust Explain what is meant by the statements that the t test for a claim about$\mu$is robust, but the$\mu$test for a claim about${\sigma }^2$is not robust.

It is given that the t test for a claim about $\mu$ is robust, but the ${\chi }^2$ test for a claim about ${\sigma }^2$ is not robust.

If the distribution of the test statistic is robust, it implies that the distribution is not very strict about the requirement of the population to be normally distributed. The test will work fine even if the population is not exactly normally distributed and the considered sample size is large.

And if the distribution of the test statistic is not robust, it means the opposite.

Here, the t test works well if the sample is from a population that is not perfectly normally distributed.

The chi-square test is not robust against deviations from normality, which means it does not work well if the population is not perfectly normally distributed.