Developing the Concept of Confidence Interval--Low Tech and High Tech

• Activity Number: 360
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Education*
• Author(s): Murray Siegel*+
• Affiliation(s): Sam Houston State University
• Keywords: confidence interval ; graphing calculator

Abstract

A difficult concept in an introductory course is confidence interval. Students use a graphing calculator to produce the results of 40 samples, each of size 30, drawn from a binomial population. Each student uses a different probability of success, "p". An 80% box plot is produced for each p. The students determine a "cutoff" value for the ends of the box, so that no more than four samples (10%) are outside the box at each end. A graph is produced where the x-axis is X, the number of successes, and the y-axis is p. Each student reports his or her p and the two cutoff values. The graph displays the intervals for each value of p that define the likely (80%) sample results. A result from a sample of 30 is presented to the class. The class must find the values of p for which the sample result is likely.

After the formulas for the various types of confidence intervals are developed, students are given two small bags of M&Ms candies and asked to determine a 90% confidence interval for the proportion of brown candies in each bag. The manufacturer claims that 30% of the candies produced are brown. Approximately ten percent of the intervals computed will not contain 30%.