Resource Library

Using a parameter it's possible to represent a property of an entire population with a single number instead of millions of individual data points. There are a number of possible parameters to choose from such as the median, mode, or interquartile range. Each is calculated in a different manner and illuminates the data from a different point of view. The mean is one of the most useful and widely used and helps us understand populations. A population is simulated by generating 10,000 floating point random numbers between 0 and 10. Sample means are displayed in histograms and analyzed.

This lesson plan uses the Birthday Paradox to introduce basic concepts of probability. Students run a Monte Carlo simulation using the TI-83 graphing calculator to generate random dates, and then search for matching pairs. Students also perform a graphical analysis of the birthday-problem function. Key Words: Permutations; Explicit Function; Recursive Function; Modeling.

An independent, nonpartisan resource on trends in American public opinion. Gives examples of recent polls, margins of error, questions asked, and sample sizes.

This Flash applet provides an introduction to simple linear regression for introductory statistics students. It combines a brief narrated animation with an interactive scatterplot function. Students are able to place points on the scatterplot by clicking with a mouse or typing X-Y coordinates. Students use these points to learn about the best fit line by placing a guess on the plot and comparing it with the least squares line. Students also learn about the value of the correlation coefficent and points that would be considered outliers. Students may also specify a value of x (within the range of the data) and obtain the resulting predicted value.

This is a virtual spinner applet, which allows you to change spinner regions and the number of spins. It records the results and displays the data in a histogram.

This is a virtual applet, which models repeaded coin tossing by a random number generator. It allows you to change the number of tosses as well as runs and records your results.

This article describes an interactive activity illustrating sampling distributions for means, properties of confidence intervals, properties of hypothesis testing, confidence intervals for means, and hypothesis tests for means. Students generate and analyze data and through simulation explore these concepts. The activity is completed in three parts. The three parts of the activity can be used in sequence or they can be used individually as "stand alone" activities. This allows the educator flexibility in utilizing the activity. Part I illustrates the sampling distribution of the sample mean. Part II illustrates confidence intervals for the population mean. Part III illustrates hypothesis tests for the population mean. This activity is appropriate for use in an introductory college or high school AP statistics course. Key words: sampling distribution of a sample mean, confidence interval for a mean, hypothesis test on a mean, simulation, random rectangles

This activity provides students with 24 histograms representing distributions with differing shapes and characteristics. By sorting the histograms into piles that seem to go together, and by describing those piles, students develop awareness of the different versions of particular shapes (e.g., different types of skewed distributions, or different types of normal distributions), that not all histograms are easy to classify, that there is a difference between models (normal, uniform) and characteristics (skewness, symmetry, etc.). Key words: Histogram, shape, normal, uniform, skewed, symmetric, bimodal

This article describes an interactive activity illustrating general properties of hypothesis testing and hypothesis tests for proportions. Students generate, collect, and analyze data. Through simulation, students explore hypothesis testing concepts. Concepts illustrated are: interpretation of p-values, type I error rate, type II error rate, power, and the relationship between type I and type II error rates and power. This activity is appropriate for use in an introductory college or high school statistics course. Key words: hypothesis test on a proportion, type I and II errors, power, p-values, simulation

This activity leads students to appreciate the usefulness of simulations for approximating probabilities. It also provides them with experience calculating probabilities based on geometric arguments and using the bivariate normal distribution. We have used it in courses in probability and mathematical statistics, as well as in an introductory statistics course at the post-calculus level. Students are expected to approximate the solution through simulation before solving it exactly. They are also expected to employ graphical as well as algebraic problem-solving strategies, in addition to their simulation analyses. Finally, students are asked to explain intuitively why it makes sense for the probabilities to change as they do. Key words: simulation, probability, geometry, independence, bivariate normal distribution