CHAPTER 13 Chi-Square applications to accompany Introduction to business statistics fourth edition by ronald M. Weiers Presentation by Priscilla Chaffe-Stengel Donald n tenge o 2002 The Wadsworth Group
CHAPTER 13 Chi-Square Applications to accompany Introduction to Business Statistics fourth edition, by Ronald M. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. Stengel © 2002 The Wadsworth Group
l 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 Tests comparing proportions from multiple populations Tests of a single population variance o 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 – Tests comparing proportions from multiple populations – Tests of a single population variance. © 2002 The Wadsworth Group
l Chapter 13-Key Terms Observed versus expected frequencies Number of parameters estimated, m Number of categories used, k Contingency table Independent variables o 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
l Goodness-of-Fit Tests The Question: Does the distribution of sample data resemble a specifie probability distribution, such as > the binomial h ypergeometric, or Poisson discrete distributions >> the uniform, normal, or exponential continuous distributions >>a predefined probability distribution ypotheses Ho: T-values expected H: f* values expected where丌 o 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 values expected where p j = 1 . © 2002 The Wadsworth Group
l Goodness-of-Fit Tests Rejection regions 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 T is known, so df =k-1 m=1 when T is unknown, so df=k-2 Poisson: m=1 since u usually estimated df =k-2 Normal: m=2 when u and o estimated df=k-3 Exponential: m= 1 since u usually estimated df=k-2 o 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