The Decision Sciences Journal of Innovative Education

A Study of the Statistical Inference Criteria:

Can We Agree on When to use Z Versus t?  

Ceyhun Ozgur

Professor of Information and Decision Sciences

College of Business Administration

Valparaiso University

Valparaiso, Indiana 46383

Tel: (219) 464-5178

E-mail: Ceyhun.Ozgur@Valpo.edu

(Corresponding Author)

Sandra E. Strasser

Associate Professor of Information and Decision Sciences

College of Business Administration

Valparaiso University

Valparaiso, Indiana 46383

Tel: (219) 464-5406

E-mail: Sandy.Strasser@Valpo.edu

          Abstract:

Authors who write introductory business statistics texts do not agree on when to use a t distribution and when to use Z 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.

Key words: Confidence intervals, hypotheses tests, teaching statistics, t distribution, Z distribution