© 2008 The Authors Teaching Statistics. Volume 30, Number 2, Summer 2008 • 53 Journal compilation © 2008 Teaching Statistics Trust Blackwell Publishing Ltd Oxford, UK TEST Teaching Statistics 0141-982X © 2007 The Authors Journal compilation © Teaching Statistics Trust XXX Original Articles Teaching Confidence Intervals Using Simulation KEYWORDS: Teaching; Confidence Intervals; Simulation; Visual Basic; Microsoft Excel. Reidar Hagtvedt Georgia Institute of Technology, USA. Gregory Todd Jones Georgia State University, USA. Kari Jones University of Georgia, USA. e-mail: lawgtj@langate.gsu.edu Summary Confidence intervals are difficult to teach, in part because most students appear to believe they understand how to interpret them intuitively. They rarely do. To help them abandon their misconcep- tion and achieve understanding, we have developed a simulation tool that encourages experimentation with multiple confidence intervals derived from the same population.  INTRODUCTION  W hen estimating parameters, students intuitively understand the need to use such language as ‘approximately’ because they don’t have any expectation that the statistic will be identical to the parameter of interest. However, they have difficulty describing what ‘approximately’ means. Students immediately see that an interval estimate might inspire more faith, particularly where this interval captures the parameter of interest a large percentage of the time. But they rarely grasp that such a confidence level either captures the para- meter or it doesn’t. Instead students typically believe that a given parameter is contained in a confidence interval with a known probability. In fact, when evaluating students prior to the instruction described in this article, zero out of thirty were able to offer a correct interpretation. Students routinely confuse probability and confidence when first learning about interval estimation, and this presents at least three pedagogical challenges. First, while it is obvious to most students that point estimates will usually miss the mark and that there would therefore be benefit to quantifying our faith in these estimates, these same students are most often at a loss for how to construct and inter- pret such measures. Second, deriving the form of confidence intervals using probability statements seems fairly straightforward – in essence merely a probability statement about given μ, Students often need a great deal of reinforcement of these ideas before they come easily. Third, understanding repeated sampling in the abstract is most often an uphill battle for students, and they are slow to develop a feel for the role of the sample in shifting the confidence interval with each repetition. Traditionally, statistics textbooks use some variant of the illustration shown in figure 1 to illustrate how different samples generate different confidence intervals. While helpful, this static image falls short of illuminating the dynamic relationship between repeated samples and confidence intervals. That is, actually observing a resampling process that shifts X P z z P z z ( ) ( ) / / / / μ σ μ σ α σ μ σ α α α α α - ≤ ≤ + ≥ - - ≤ ≤ + ≥ - 2 2 2 2 1 1 X X X X X X X ⇕