# Algebra level symbolic math

• ### Psychic test

This activity illustrates the convergence of long run relative frequency to the true probability. The psychic ability of a student from the class is studied using an applet. The student is asked to repeatedly guess the outcome of a virtual coin toss. The instructor enters the student's guesses and the applet plots the percentage of correct answers versus the number of attempts. With the applet, many guesses can be entered very quickly. If the student is truly a psychic, the percentage correct will converge to a value above 0.5.
• ### Using Your Hair to Understand Descriptive Statistics

The purpose of this activity is to enhance students' understanding of various descriptive measures. In particular, by completing this hands-on activity students will experience a visual interpretation of a mean, median, outlier, and the concept of distance-to-mean.
• ### A ducks story- introducing the idea of testing (statistical) hypotheses

By means of a simple story and a worksheet with questions we guide the students from research question to arriving at a conclusion. The whole process is simply reasoning, no formulas. We use the reasoning already done by the student to introduce the standard vocabulary of testing statistical hypotheses (null & alternative hypotheses, p-value, type I and type II error, significance level). Students need to be familiar with binomial distribution tables. After the ducks story is finished, the class is asked to come up with their own research question, collect the data, do the hypotheses testing and answer their own research question. The teaching material is intended to be flexible depending of the time available. Instructors can choose to do just the interactive lecture type, interactive lecture + activity, or even add the optional material.
• ### 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.
• ### **One-way ANOVA Demonstration

Tutorial on the ANOVA test in statistics and probability, with a description, formulas, example, and a calculator applet. This is part of the larger site Virtual Statistician at http://web.mst.edu/~psyworld/virtualstat.htm
• ### Song: Stat 51: I Will Survive

Song about the use of the 5-number summary to describe skewed data as an alternative to the mean and standard deviation. May be sung to the tune of the 1979 song "I Will Survive" by Gloria Gaynor. Lyrics written by Sheila O'Leary Weaver. The song took first place in the song category in the 2007 A-Mu-Sing competition. Musical accompaniment realization are by Joshua Lintz and vocals are by Mariana Sandoval from University of Texas at El Paso.

• ### Song: MLE

Song about the properties of Maximum Likelihood Estimation including efficiency, invariance, and asymptotic normality. May sing to the tune of "Let it Be" By Paul McCartney. Recorded June 26, 2009 at the OSU Whisper Room: Larry Lesser, vocals/guitar; Justin Slauson, engineer.

• ### Cartoon: Mouse Differences

A cartoon to teach how statistics helps to isolate the underlying causes behind the difference between comparison groups. 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.
• ### Cartoon: Survey Humor

A cartoon for general use with discussions of election polls. Cartoon by John Landers (www.landers.co.uk) based on an idea from Steve MacEachern (The Ohio State University). Free to use in the classroom and on course web sites.