Classroom Simulation: The Margin of Error in a Public Opinion Poll

• Activity Number: 74
• Type: Contributed
• Date/Time: Sunday, August 7, 2005 : 8:00 PM to 9:50 PM
• Sponsor: Section on Statistical Education
• Author(s): Bruce E. Trumbo*+ and Eric Suess and Shuhei Okumura
• Companies: California State University, East Bay (Hayward Hills Campus) and California State University, East Bay (Hayward Hills Campus) and California State University, Hayward
• Keywords: Public opinion poll ; Margin of error ; Simulation ; Feller arcsine law ; Teaching ; R / S-Plus

Abstract

Appropriate simulations can be used effectively in a beginning statistics course to illustrate important principles---either before the underlying theory is accessible or along with a presentation of the theory. Here, we use few fundamental functions in R to illustrate the margin of error of a public opinion poll. Polls using 25 and 2500 subjects from a population with a known pro-portion "in favor" are simulated repeatedly. Summaries of results illustrate point estimates of the proportion in favor are variable and approximately nor-mally distributed and that errors are smaller for the larger number of subjects. Interval estimates are discussed. A slightly more advanced simulation illustrates that, during the process of a poll, the proportion of steps at which the running fraction in favor is higher than the population probability is much more likely to be near 0 or 1 than to be near half, following Feller's arcsine law (a "bathtub shaped" beta distribution).