A Normality Test for the Mean Estimator

This note proposes a tool to investigate and demonstrate the adequacy of the central limit theorem in small samples. The suggested testing procedure provides a method to investigate if the mean estimator is approximately normally distributed, given data and sample size at hand. This is important when deciding upon inference procedure, i.e. is parametric inference possible or do we have to settle for nonparametrics. The procedure is well-suited for teaching in under-graduate statistics classes.