# Elementary Probability

• ### Cartoon: The Lottery

A cartoon to teach ideas of elementary probability. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University) in 2008. Free to use in the classroom and on course web sites.

• ### Cartoon: Thomas Jefferson's Motivation

A cartoon to teach ideas of conditional probability. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University) in 2008. Free to use in the classroom and on course web sites.

• ### Simulating the Effect of Sample Size on the Sampling Distribution of the Mean

This activity allows students to explore the relationship between sample size and the variability of the sampling distribution of the mean. Students use a Java applet to specify the shape of the "parent" distribution and two sample sizes. The simulation then samples from the parent distribution to approximate the sampling distributions for the two sample sizes. Students can see both sampling distributions at the same time making them easy to compare. The activity also allows students to determine the probability of extreme sample means for the different sample sizes so that they can discover that small sample sizes are much more likely than large samples to produce extreme values. Keywords: sampling distribution, sample size, simulation
• ### An In-Class Experiment to Estimate Binomial Probabilities

This hands-on activity is appropriate for a lab or discussion section for an introductory statistics class, with 8 to 40 students. Each student performs a binomial experiment and computes a confidence interval for the true binomial probability. Teams of four students combine their results into one confidence interval, then the entire class combines results into one confidence interval. Results are displayed graphically on an overhead transparency, much like confidence intervals would be displayed in a meta-analysis. Results are discussed and generalized to larger issues about estimating binomial proportions/probabilities.
• ### Independent Samples t-Test: Chips AhoyŒ¬ vs. Supermarket Brand

In this hands-on activity, students count the number of chips in cookies in order to carry out an independent samples t-test to see if Chips AhoyŒ¬ cookies have a higher, lower, or different mean number of chips per cookie than a supermarket brand. First there is a class discussion that can include concepts about random samples, independence of samples, recently covered tests, comparing two parameters with null and alternative hypotheses, what it means to be a chip in a cookie, how to break up the cookies to count chips, and of course a class consensus on the hypotheses to be tested. Second the students count the number of chips in a one cookie from each brand, and report their observations to the instructor. Third, the instructor develops the independent sample t-test statistic. Fourth, the students carry out (individually or as a class) the hypothesis test, checking the assumptions on sample-size/population-shape.
• ### Quote: Pasteur on Chance

In the fields of observation chance favors only the prepared mind. A quote from French chemist and microbiologist Louis Pasteur (1822 - 1895) given at a lecture at University of Lille on December 7, 1854.

• ### Video: Statistically Speaking

Statistically Speaking is a 5 minute 35 second video that can be used in discussing various concepts in descriptive statistics. The video was written, directed, and produced by Cameron W. Hatch and the cast includes (order of appearance) Mala Grewal, Sally Atkinson, Griffin Hatch, Jeff Hatch, Matt Burnham, and Sylvia Burnham.

• ### Cartoon: The T-distribution Family

A cartoon to teach about the family of t-distributions including their relationship to the normal distribution. Cartoon by John Landers (www.landers.co.uk) based on an idea and sketch from Sheila O. Weaver (University of Vermont). This is part of a three cartoon set that took first place in the cartoon category of the 2007 A-Mu-sing competition. Free to use in the classroom and on course web sites.

• ### Cartoon: Divorce Lawyers

A cartoon for teaching about probability rules for disjoint events and how they do not apply to events that overlap. Cartoon by John Landers (www.landers.co.uk) based on an idea from Paul Rosile (Franklin County, Ohio Board of Health). Free to use in the classroom and on course web sites.
• ### Cartoon: Statistical Qualifications

A cartoon to teach about proper reporting of statistical results such as conclusions from a significance test. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites.