The negative hypergeometric distribution is often not formally studied in secondary or collegiate statistics in contexts other than drawing cards without replacement. We present a different context with the potential of engaging students in simulating and exploring data.

Research shows that students often struggle with understanding empirical sampling distributions. Using hands-on and technology models and simulations of problems generated by real data help students begin to make connections between repeated sampling, sample size, distribution, variation, and center. A task to assist teachers in implementing…

One econometric rule of thumb is that greater dispersion in observations of the independent variable improves estimates of regression coefficients and therefore produces better results, i.e., lower standard errors of the estimates. Nevertheless, students often seem to mistrust precisely the observations that contribute the most to this greater…

There is considerable research on the difficulties students have in conceptualising individual concepts of probability and statistics (see for example, Bryant & Nunes, 2012; Jones, 2005). The unit of work developed for the action research project described in this article is specifically designed to address some of these in order to help…

For many students meeting, say, the gamma distribution for the first time, it may well turn out to be a rather fruitless encounter unless they are immediately able to see an application of this probability model to some real-life situation. With this in mind, we pose here an appealing problem that can be used as the basis for a workshop activity…

Students learn to examine the distributional assumptions implicit in the usual t-tests and associated confidence intervals, but are rarely shown what to do when those assumptions are grossly violated. Three data sets are presented. Each data set involves a different distributional anomaly and each illustrates the use of a different nonparametric…

This study serves as a teaching aid for teachers of introductory statistics. The aim of this study was limited to determining various sample sizes when estimating population proportion. Tables on sample sizes were generated using a C[superscript ++] program, which depends on population size, degree of precision or error level, and confidence…

Null distributions of permutation tests for two-sample, paired, and block designs are simulated using the R statistical programming language. For each design and type of data, permutation tests are compared with standard normal-theory and nonparametric tests. These examples (often using real data) provide for classroom discussion use of metrics…

On the 2009 AP[c] Statistics Exam, students were asked to create a statistic to measure skewness in a distribution. This paper explores several of the most popular student responses and evaluates which statistic performs best when sampling from various skewed populations. (Contains 8 figures, 3 tables, and 4 footnotes.)

This article provides a historical context for the debate between Georg Cantor and Leopold Kronecker regarding the cardinality of different infinities and incorporates the short story "Welcome to the Hotel Infinity," which uses the analogy of a hotel with an infinite number of rooms to help explain this concept. Wanko makes use of this history and…

This article looks at a process of integrating real-life data investigation in a course on descriptive statistics. Referring to constructivist perspectives, this article suggests a look at the potential of inculcating alternative teaching methods that encourage students to take a more active role in their own learning and participate in the…

The ubiquitous change jar (or any other container) is the focus of this investigation. Using random pocket change, a distribution is determined and statistical tools are employed to calculate the value of given volumes of coins. This brief investigation begins by considering money, which piques the interest of most students, and uses this…

The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The modules also introduce students to real world math concepts and problems that property and casualty actuaries come across in their work. They are designed to be used by teachers and…

Emphasis on problem solving in mathematics has gained considerable attention in recent years. While statistics teaching has always been problem driven, the same cannot be said for the teaching of probability where discrete examples involving coins and playing cards are often the norm. This article describes an application of simple probability…

During the last decade the use of Bayesian statistical method has become quite prevalent in the educational community. Yet, like most statistical techniques, little has been written concerning the application of these methods to the classroom setting. The purpose of this paper is to help correct such a deficiency in the literature by developing a…