Chapter 3 Constructing Statistical Intervals Assuming a Normal Distribution Using Simple Tabulations

Objectives and Overview

This chapter presents, tabulates, and compares factors for calculating the different kinds of intervals, based upon a sample of size n from a normal distribution with unknown mean μ and unknown standard deviation σ. Specifically, we present factors for:

  • Two-sided confidence intervals and one-sided confidence bounds to contain the distribution mean μ and the distribution standard deviation σ.
  • Two-sided tolerance intervals and one-sided tolerance bounds to contain at least a proportion β of the distribution values, for β = 0.90, 0.95, and 0.99.
  • Two-sided prediction intervals and one-sided prediction bounds to contain the values of all of m = 1, 2, 5, 10, 20, and m = n randomly selected future observations, and the sample mean and standard deviation of m = n future observations.

For each kind of interval or bound, the tables provide factors for both 95% and 99% confidence levels. We also present examples illustrating the use of these factors.

The chapter presents:

  • The normal distribution, justification for its use, and background information about the factors (Section 3.1).
  • The circuit pack voltage application that will be used to illustrate the use of the factors (Section 3.2).
  • Use of the factors for two-sided statistical intervals (Section 3.3).
  • Use of the factors for one-sided statistical bounds (Section 3.4).

3.1 Introduction

3.1.1 The Normal ...

Get Statistical Intervals, 2nd Edition now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.