A Study of the Statistical Inference Criteria: Can We Agree on When to use Z Versus t?

Authors who write introductory business statistics texts do not agree on when to use a t distribution and when to use a Z distribution in both the construction of confidence intervals and the use of hypothesis testing. In a survey of textbooks written in the last 15 years, we found the decision rules to be contradictory and, at times, the explanations unclear. This paper is an attempt to clarify the decision rules and to recommend that one consistent rule be chosen to minimize confusion to students, instructors, and practitioners. Using the t distribution whenever σ is unknown, regardless of sample size, seems to provide the best solution both theoretically and practically.