Comparison of Intervals

Abstract : One of the fascinating and fun aspects of statistics is the many approaches that can be used to solve the same problem. These varied approaches often have very subtle differences. In this paper, we were interested in finding out if all 18 ounce bags of Chips Ahoy! cookies contain more than 1000 chips. We first collected bags of cookies from across the United States and then extracted the chips in 42 randomly selected bags. For the analysis, we looked at confidence intervals, prediction intervals for a single bag, tolerance intervals (parametric and distribution-free), and a bootstrap confidence bound for the proportion of bags exceeding the specified 1000 chips (for an excellent discussion of the different types of intervals see Hahn and Meeker).