AI-Supported Interactive Simulation to Teach Statistical Hypothesis Testing: Case of the Point Optimal Test and Power Envelope for the Cauchy Distribution

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.