Statistical Intervals, 2nd Edition

Chapter 11 Basic Case Studies

Objectives and Overview

This chapter presents a series of case studies that illustrate the methods in the first 10 chapters of this book. They are a representative sample of frequently occurring problems that we have encountered recently. We present these problems as they were presented to us, rather than in a “clean” textbook style. Then we describe our proposed solution. We stress the basic underlying assumptions and the practical aspects of using and interpreting statistical intervals.

We illustrate some of the most important topics covered in the earlier chapters. Thus, there is some repetition of techniques, but each example has some new feature. In some of the case studies we compare different approaches for answering a question. In one example we use methods from Section 4.5 to estimate the probability that an observation will exceed a threshold, assuming that the data came from a normal distribution. Then, without making the normal distribution assumption, we show how to estimate the same probability by using as data only the number of observations that exceed the threshold (a nonparametric method using binomial distribution methods from Section 6.2).

The following applications are discussed in this chapter:

• Demonstration that the operating temperature of most manufactured devices will not exceed a specified value (Section 11.1).
• Forecasting future demand for spare parts (Section 11.2).
• Estimating the probability of passing an environmental ...