Impossible Inferences: A Note on Inconsistency in Business Statistics

Textbooks designed for business statistics customarily present inferential statistics whose premises contradict the definitions developed in descriptive statistics. In particular, because the standard deviation of a population cannot be calculated if the population mean is unknown, hypothesis tests and confidence intervals for the mean that rely on the population standard deviation pose an inconsistency between lessons. To reduce potential confusion and utilize both class time and students’ homework time efficiently, the present note proposes de-emphasizing these tests and intervals in favor of those that depend on the sample standard deviation.