Probability in Action: the Red Traffic Light

John A. Shanks University of Otago
Journal of Statistics Education Volume 15, Number 1 (2007),

Abstract

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 distributions to a practical problem involving a car’s approach to a red traffic light, and draws on the ideas of density functions, expected value and conditional distributions. It provides a valuable exercise in applying theory in a practical context.

Keywords: Distributions; Modelling; Optimization; Problem solving.

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A Bubble Mixture Experiment Project for Use in an Advanced Design of Experiments Class

Stefan H. Steiner - University of Waterloo
Michael Hamada - Los Alamos National Laboratory
Bethany J. Giddings White - University of Waterloo
Vadim Kutsyy - Guardian Analytics
Sofia Mosesova - University of Waterloo
Geoffrey Salloum - Camosun College

Journal of Statistics Education Volume 15, Number 1 (2007)

Abstract

This article gives an example of how student-conducted experiments can enhance a course in the design of experiments. We focus on a project whose aim is to find a good mixture of water, soap and glycerin for making soap bubbles. This project is relatively straightforward to implement and understand. At its most basic level the project introduces students to mixture experiments and general issues in experimental design such as choosing and measuring an appropriate response, selecting a design, the effect of using repeats versus replicates, model building, making predictions, etc. To accommodate more advanced students, the project can be easily enhanced to draw on various areas of statistics, such as generalized linear models, robust design, and optimal design. Therefore it is ideal for a graduate level course as it encourages students to look beyond the basics presented in class.

Keywords: Constrained experimental region; Generalized linear model; Optimal design; Poisson regression; Robust parameter design.

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Oil and Gas on Indian Reservations: Statistical Methods Help to Establish Value for Royalty Purposes

Mary S. Fowler

Worcester State College

Joseph B. Kadane

Carnegie Mellon University
Journal of Statistics Education Volume 14, Number 3 (2006), www.amstat.org/publications/jse/v14n3/kadane.html

Abstract

Part of the history of oil and gas development on Indian reservations concerns potential underpayment of royalties due to under-valuation of production by oil companies. This paper discusses a model used by the Shoshone and Arapaho tribes in a lawsuit against the Federal government, claiming the Government failed to collect adequate royalties. Portions of the case have been settled out of court with compensation paid to the Tribes. Other portions remain pending. This material can be used as a real example in a calculus-based probability and statistics course.

Keywords: Expectation; Law; Location-scale family.

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