Statistical Intervals, 2nd Edition

Chapter 10 Sample Size Requirements for Prediction Intervals

Objectives and Overview

This chapter provides guidelines for choosing the sample size required to obtain a prediction interval to contain a future single observation, a specified number of future observations, or some other quantity to be calculated from a future sample from a previously sampled distribution. The topics discussed in this chapter are:

• The factors that determine the width of a prediction interval (Section 10.1).
• Sample size determination for a normal distribution prediction interval (Section 10.2).
• Sample size determination for a distribution-free prediction interval for at least k of m future observations (Section 10.3).

10.1 Prediction Interval Width: The Basic Idea

There are two sources of imprecision in statistical prediction: First, there is the random variation in the future sample. Second, because the given data are limited, there is uncertainty with respect to the characteristics (e.g., parameters) of the previously sampled distribution. Say, for example, that the results of an initial sample of size n from a normal distribution with unknown mean μ and unknown standard deviation σ are to be used to predict the value of a single future randomly selected observation from the same distribution. The sample mean of the initial sample will be used to predict the future observation. First, , where ...