By Won chul Song (Milwaukee School of Engineering)
Information
At our institution, we offer a probability and statistics course for engineering students that meets ABET requirements. This course typically enrolls about 25 students. While students often demonstrate proficiency in the probability section without issue, they often face challenges in demonstrating proficiency once we move to statistical inference. To address this concern, I have developed simulation-based activities using R with real-world data to support students' understanding of statistical inference for learning the Central Limit Theorem (CLT) and the confidence interval. For example, students run repeated random simulations of the coin flips using a binomial distribution with different probabilities of success to demonstrate the CLT. Students then construct a histogram to observe the change in shape as the number of trials increases. Another example is to construct a confidence interval by taking a random sample of used car data from a popular online car listing site. Students repeat the process to observe the number of times the confidence interval contains the true population mean. However, we found that the open-ended questions we designed to encourage deeper thinking about their observations were often only answered superficially without further exploration. For this reason, I have revised the questions to guide students to specifically see the connections between the outcome of the simulation and the inference topics they are learning. Students’ responses in the guided activities show an improvement in their understanding of the statistical inference when compared to the simple open-ended questions.