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

Music City Center 

This talk advocates for a conceptually grounded approach to teaching hypothesis testing in introductory statistics courses, particularly in the context of one-sided tests for mean and proportion inference. While standard instructional materials typically present the null hypothesis as an equality regardless of whether a test is one-sided or two-sided, we propose framing the null and alternative as complementary hypotheses—an approach that naturally leads to inequalities in the null for one-sided tests. This framing aligns with the Neyman-Pearson paradigm, and enhances conceptual clarity for students. Through a review of mainstream introductory textbooks, we examine how key concepts such as the null hypothesis and significance level are commonly presented, and offer refinements. We demonstrate that defining the null as an inequality allows for a more precise treatment of the Type I error. To support instruction, we present a classroom activity that guides students in discovering this property through empirical and visual means. Our approach preserves procedural simplicity while deepening students' understanding of core inferential ideas.

Teaching hypothesis testing

mean and proportion inference

introductory statistics

Type I error

significance level,

class activity 

Section on Statistics and Data Science Education