Understanding the Central Limit Theorem the Easy Way: A Simulation Experiment

Abstract

Using a simulation approach, and with collaboration among peers, this paper is intended to improve the understanding of sampling distributions (SD) and the Central Limit Theorem (CLT) as the main concepts behind inferential statistics. By demonstrating with a hands-on approach how a simulated sampling distribution performs when the data used has different probability distributions, we expect to clarify the notion of the Central Limit Theorem, and the use of samples in the hypothesis testing process for populations. This paper will discuss an initial stage to create random samples from a given population (using Excel) with collaboration of the students, which has been tested in the classroom. Then, based on that experience, a second stage in which we created an online simulation, controlled by the professor, and in which the students will participate during class time using an electronic device connected to internet. Students will create simple random samples from a variety of probability distributions simulated online in a collaborative way. Once the samples are generated, the instructor will combine and summarize the resulting sample statistics using histograms and the results will be discussed with the students. The objective is to teach some of the central topics of introductory statistics, the Central Limit Theorem and sampling distributions with an interactive and engaging approach.

Keywords

• Central Limit Theorem
• simulation
• sampling distribution
• random samples
• approximation to normality