AI-supported interactive simulation to teach statistical hypothesis testing: Case of the point optimal test and power envelope for the Cauchy distribution

Abstract

Teaching complex statistical concepts like the Neyman–Pearson Lemma and Point Optimal testing is often hindered by their mathematical abstraction. To facilitate the learning process, education technology researchers offer interactive, simulation-based, technology-enhanced teaching solutions. Thus, this paper presents an AI-supported interactive simulation module, integrated into a university Learning Management System (Canvas LMS), to bridge the gap between rigour and comprehension. Using the location parameter of a Cauchy distribution as a case study, it is demonstrated how students can dynamically visualize shifting rejection regions and power envelopes in real time. The module employs a reinforcement-learning-based engine to analyse learner interactions, providing adaptive hints that address specific misconceptions regarding distributional symmetry and test efficiency. Preliminary implementation in advanced econometrics courses indicates that this interactive, AI-driven learning and teaching approach significantly improves conceptual understanding and student engagement by transforming static theory into an exploratory learning experience.