1. Applications of the Chi-Square Statistic Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

2. The Binomial Situation The experiment consists of n repetitions(trials). The trials are independent. Each trial has two possible outcomes (success, failure). The probability of a success for each trial is p. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

3. H o : p = p o versus H a : p  p o H o : p 1 =.04 p 2 =.96 H a : p 1 .04 p 2 .96 Reject H o if  2 >  2.05,1 = 3.84 Lot Sampling Example Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

4. Lot Sampling Example 8.51 > 3.84 therefore we reject H o We conclude that the proportion of defectives is not.04 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

5. The Multinomial Situation Assumptions The experiment consists of n independent repetitions. Each trial outcome falls in exactly one of k categories. The probabilities of the k outcomes are denoted by p 1, p 2,..., p k and remain the same on each trial. Further: p 1 + p 2,+...+ p k = 1 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

6. Hypothesis Testing for the Multinomial Situation Where: 1. The summations is across all categories 2. The O’s are the observed frequencies in each category using the sample. 3. The E’s are the expected frequencies in each category if H o is true. 4. The df for the chi-square statistic are k-1, where k is the number of categories. Introduc tion to Busines s Statistic s, 5e Kvanli/ Guynes/ Pavur (c)2000 South- Western College Publishi ng

7. Chi-Square Test of Independence Null and Alternative Hypothesis H o : the classifications are independent H a : the classifications are dependent Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

8. Chi-Square Test of Independence Estimating the Expected Frequencies Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

9. Expected Frequencies Figure 13.4 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

10. Chi-Square Test of Independence Estimating the Expected Frequencies Example Age Sex 45Total Male 60 20 40 (30) 120 Female 40 30 10 80 Total100 50 50 200 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing Estimate for Male and Over 45

11. Chi-Square Test of Independence The Testing Procedure H o : the row and column classifications are independent H a : the row and column classifications are dependent Reject H o if  2 >  2. ,df where df = (r-1)(c-1) Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

12. Chi-Square Test of Independence The Testing Procedure The test statistic is Where: 1. The summation is over all cells of the contingency table 2. O is the observed frequency 3. E is the expected frequency 4. The degrees of freedom are df = (r-1)(c-1) Introduc tion to Busines s Statistic s, 5e Kvanli/ Guynes/ Pavur (c)2000 South- Western College Publishi ng