Unraveling the Mystery of Equality in the Null Hypothesis: How Using Inequality Enhances Conceptual Understanding of Hypothesis Testing for our Introductory Students

This paper recommends a refinement in teaching hypothesis testing in introductory, non-calculus-based statistics courses, focusing on how the null hypothesis is formulated in mean and proportion inference. The proposal is grounded in classroom experience at CSU Fullerton, where general education courses enroll liberal arts and natural science students in lecture–lab formats. Most mainstream textbooks at this level (e.g., Peck, Gould, De Veaux) present the null as an equality for one-sided tests. Instead, we suggest adopting the Neyman–Pearson framework, commonly used in mathematical statistics textbooks, which treats the null and alternative as complementary hypotheses, leading to an inequality in the null in one-sided tests. Framing the hypotheses in this way is more logical to students, allows fundamental hypothesis testing concepts such as Type I error and significance level to be taught more precisely, and helps students recognize the uncertainties inherent in hypothesis testing rather than viewing it as a purely algorithmic process. To support instructor implementation, we provide a classroom activity accompanied by an interactive Shiny app that allows students to explore Type I error probabilities empirically and visually. This pedagogical framework is consistent with GAISE recommendations to teach statistical thinking, focus on conceptual understanding, and use technology to explore ideas.