Conceptual issues in quantifying unusualness and conceiving stochastic experiments: Insights from students' experiences in designing sampling simulations

Abstract

This article reports on a classroom teaching experiment that engaged a group of high school students in designing sampling simulations within a computer microworld. The simulation-design activities aimed to foster students' abilities to conceive of contextual situations as stochastic experiments, and to engage them with the logic of hypothesis testing. This scheme of ideas involves imagining a population and a sample drawn from it, and an image of repeated sampling as a basis for quantifying a sampling outcome's unusualness in terms of long-run relative frequency under an assumption about the population's composition. The study highlights challenges that students experienced, and sheds light on aspects of conceiving stochastic experiments and conceiving a sampling outcome's unusualness as a probabilistic quantity.