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Variance and Decision-making Approach

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Variance and Decision-making Approach
Business Statistics:
A Decision-Making Approach
7th Edition

Chapter 11
Hypothesis Tests and Estimation for Population Variances

Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.

Chap 11-1

Chapter Goals
After completing this chapter, you should be able to:








Formulate and complete hypothesis tests for a single population variance
Find critical chi-square distribution values from the chi-square table
Formulate and complete hypothesis tests for the difference between two population variances
Use the F table to find critical F values

Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.

Chap 11-2

Hypothesis Tests for Variances
Hypothesis Tests for Variances

Tests for a Single
Population Variance

Tests for Two
Population Variances

Chi-Square test statistic

F test statistic

Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.

Chap 11-3

Single Population
Hypothesis Tests for Variances

Tests for a Single
Population Variance

*

Chi-Square test statistic

Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.

H0: σ2 = σ02
HA: σ2 ≠ σ02

Two tailed test

H0: σ2  σ02
HA: σ2 < σ02

Lower tail test

H0: σ2 ≤ σ02
HA: σ2 > σ02

Upper tail test

Chap 11-4

Chi-Square Test Statistic
Hypothesis Tests for Variances
The chi-squared test statistic for a Single Population Variance is:

Tests for a Single
Population Variance

Chi-Square test statistic

(n  1)s

2 σ 2

*

2

where
2 = standardized chi-square variable n = sample size s2 = sample variance σ2 = hypothesized variance

Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.

Chap 11-5

The Chi-square Distribution




The chi-square distribution is a family of distributions, depending on degrees of freedom:
d.f. = n - 1

0 4 8 12 16 20 24 28
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