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8

Statistical Intervals

for a Single Sample

CHAPTER OUTLINE

LEARNING OBJECTIVES

After careful study of this chapter, you should be able to do the following:

1. Construct confidence intervals on the mean of a normal distribution, using either the normal
   distribution or the tdistribution method


2. Construct confidence intervals on the variance and standard deviation of a normal distribution


3. Construct confidence intervals on a population proportion


4. Construct prediction intervals for a future observation


5. Construct a tolerance interval for a normal population

8-1 INTRODUCTION

8-2 CONFIDENCE INTERVAL ON THE

MEAN OF A NORMAL DISTRIBU-

TION, VARIANCE KNOWN

8-2.1 Development of the Confidence

Interval and its Basic Properties

8-2.2 Choice of Sample Size

8-2.3 One-Sided Confidence Bounds

8-2.4 General Method to Derive a

Confidence Interval

8-2.5 A Large-Sample Confidence

Interval for 

8-2.6 Bootstrap Confidence Intervals

(CD Only)

8-3 CONFIDENCE INTERVAL ON THE

MEAN OF A NORMAL DISTRIBU-

TION, VARIANCE UNKNOWN

8-3.1 The tDistribution

8-3.2 Development of the tDistribution

(CD Only)

8-3.3 The tConfidence Interval on 

8-4 CONFIDENCE INTERVAL ON THE

VARIANCE AND STANDARD

DEVIATION OF A NORMAL

POPULATION

8-5 A LARGE-SAMPLE CONFIDENCE

INTERVAL FOR A POPULATION

PROPORTION

8-6 A PREDICTION INTERVAL FOR A

FUTURE OBSERVATION

8-7 TOLERANCE INTERVALS FOR A

NORMAL DISTRIBUTION

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