Question

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.

Short answer

The meaning of the given statement is that the t distribution gives accurate results about the hypothesis test even if the population is not strictly normally distributed. On the other hand, the chi-square distribution does not produce accurate result if the considered population is not strictly normally distributed.

Step-by-step solution

Given information

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.

Interpretation of the distribution being 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.