# Algebra level symbolic math

• ### **Simulating Confidence Intervals

This applet generates confidence intervals for means or proportions. The options for confidence intervals for means include "z with sigma," "z with s," or "t." The options for confidence intervals for proportions are "Wald," "Adjusted Wald," or "Score." Users set the population parameters, sample size, number of intervals, and confidence level. Click "Sample," and the applet will graph the intervals. Intervals shown in green contain the true population mean or proportion, while intervals in red do not. The true mean or proportion is shown by a blue line. The applet displays the proportion of intervals containing the population parameter for each sample and a running total of all the samples. Users can also click on a particular interval to display the numerical interval or sort the displayed confidence intervals from smallest to largest. This applet is part of a collection designed to accompany the textbook "Investigating Statistical Concepts, Applications, and Methods" (ISCAM) and is used in Exploration 4.3 on page 327, Investigation 4.3.6 on page 331, and Exploration 4.4 on page 350. This applet also supplements "Workshop Statistics: Discovery with Data," 2nd edition, Activity 19-5 on page 403. Additional materials written for use with these applets can be found at http://www.mathspace.com/NSF_ProbStat/Teaching_Materials/rowell/final/16_cireview_bc322_2.doc and http://www.mathspace.com/NSF_ProbStat/Teaching_Materials/rowell/final/15_sampdistreview_bc322_1.doc.
• ### Primer on Probability, Odds and Interpreting their Ratios

This lecture example discusses calculating chance with probabilities (a ratio of occurrence to the whole) or odds (a ratio of occurrence to nonoccurrence). It presents a clinical example of measuring the chance of initiating breastfeeding among 1000 new mothers. Tables are provided in pdf format.
• ### Primer on Type I and Type II Errors

This lecture example discusses type I and type II errors as they apply in a clinical setting.
• ### Primer on 95% Confidence Intervals

This lecture example reviews the concept of CIs and their relationship to P values. Tables are provided in pdf format.
• ### Primer on Correlation Coefficients

This lecture example discusses how two continuous variables relate to one another with a clinical example of the relationship between body mass and fasting blood sugar. It offers three questions to help readers visualize and interpret correlation coefficients.
• ### Primer on Interpreting Surveys

Because surveys are increasingly common in the medical literature, readers need to be able to critically evaluate the survey method. Two questions are fundamental: 1) Who do the respondents represent? 2) What do their answers mean? This lecture example discusses survey sampling terms and aspects of interpreting survey results.
• ### The Stat Cave Project

This NSF funded project provides worksheets and laboratories for introductory statistics. The overview page contains links to 9 worksheets that can be done without technology, which address the topics of obtaining data, summarizing data, probability, regression and correlation, sampling distributions, hypothesis testing and confidence intervals. The page also contains twelve laboratories that require the use of technology. Data sets are provided in Minitab format.
• ### Quote: Clark on Advertising

Asked about the power of advertising in research surveys, most agree that it works, but not on them. A quote by British Journalist and author Eric Clark from his book "The Want Makers: Inside the World of Advertising", Penguin Books (1988) page 13.
• ### Song: Learn to use Chance

Song calls for the importance of chance, juxtaposed a variety of statistical terms. May be sung to the tune of "Give Peace a Chance" (John Lennon). Musical accompaniment realization and vocals are by Joshua Lintz from University of Texas at El Paso.
• ### Cartoon: Raking the Lawn

A cartoon that can be used in teaching about the efficiency of using simulation in statistics. Cartoon 2006 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.