文档介绍：CHAPTER 13 Chi-Square Applications
to pany
Introduction to Business Statistics
fourth edition, by Ronald M. Weiers
Presentation by Priscilla Chaffe-Stengel
Donald N. Stengel
© 2002 The Wadsworth Group
Chapter 13 - Learning Objectives
Explain the nature of the chi-square distribution.
Apply the chi-square distribution to:
Goodness-of-fit tests
Tests of independence between 2 variables
paring proportions from multiple populations
Tests of a single population variance.
© 2002 The Wadsworth Group
Chapter 13 - Key Terms
Observed versus expected frequencies
Number of parameters estimated, m
Number of categories used, k
Contingency table
Independent variables
© 2002 The Wadsworth Group
Goodness-of-Fit Tests
The Question:
Does the distribution of sample data resemble a specified probability distribution, such as:
the binomial, hypergeometric, or Poisson discrete distributions.
the uniform, normal, or exponential continuous distributions.
a predefined probability distribution.
Hypotheses:
H0: pi = values expected H1: pi ¹ values expected
where
© 2002 The Wadsworth Group
Goodness-of-Fit Tests
Rejection Region:
Degrees of Freedom = k – 1 – m
where k = # of categories, m = # of parameters
Uniform Discrete: m = 0 so df = k – 1
Binomial: m = 0 when p is known, so df = k – 1
m = 1 when p is unknown, so df = k – 2
Poisson: m = 1 since µ usually estimated, df = k – 2
Normal: m = 2 when µ and s estimated, df = k – 3
Exponential: m = 1 since µ usually estimated, df = k – 2
© 2002 The Wadsworth Group
Goodness-of-Fit Tests
Test Statistic:
where Oj = Actual number observed in each class
Ej = Expected number, pj • n
å
=
j
E
j
E
j
O
2
)
–
(
2
c
© 2002 The Wadsworth Group
Goodness-of-Fit: An Example
Problem : In a study of vehicle ownership, it has been found that % of . households do not own a vehicle, with % owning 1 vehicle, % owning 2 vehicles, and % owning 3 or more vehicles. The data for a random sample of 100 household