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## CD-ROM Chapter 14

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**CD-ROM Chapter 14**Goodness-of-Fit Tests and Contingency Analysis**Chapter 14 - Chapter Outcomes**After studying the material in this chapter, you should be able to: • Utilize the chi-square goodness-of-fit test to determine whether data from a process fit a specified distribution. • Set up a contingency analysis table and perform a chi-square test of independence.**Chi-Square Goodness-of-Fit Test**CHI-SQUARE GOODNESS OF FIT TEST STATISTIC where: k = Number of categories oi = Observed cell frequency for category i ei = Expected cell frequency for category i**Chi-Square Goodness-of-Fit Test(Vista Health Guard Example)**H0: Patient demand is evenly spread throughout the weekdays and 25% lower on weekends. HA: Patient demand follows some other distribution. = 0.05**Chi-Square Goodness-of-Fit Test(Figure 14-3)**f(2) d.f. = k - 1 = 7 - 1 = 6 Rejection Region = 0.05 2 2 = 12.592 Decision Rule: If 2 > 12.592, reject H0 Otherwise, do not reject H0**Chi-Square Goodness-of-Fit Test(Figure 14-3)**Since 3,302.7 > 12.592, reject H0**Contingency Analysis**A contingency table is a table used to classify sample observations according to two or more identifiable characteristics. Also called a crosstabulation table.**Contingency Analysis**CHI-SQUARE CONTINGENCY TEST STATISTIC where: oij = Observed frequency in cell (i, j) eij = Expected frequency in cell (i, j) r = Number of rows c = Number of columns**Contingency Analysis(From Figure 14-9)**H0: Gender of yearbook editor is independent of college’s funding source. HA: Gender of yearbook editor is not independent of college’s funding source. = 0.05 Private Public Actual = 14 Actual = 43 Male Expected = 39.98 Expected = 17.02 Actual = 141 Actual = 23 Female Expected = 115.02 Expected = 48.98**Contingency Analysis(From Figure 14-9)**f(2) d.f. = (r - 1)(c - 1) = (1)(1) = 1 Rejection Region = 0.05 2 2 = 3.841 Decision Rule: If 2 > 3.841, reject H0 Otherwise, do not reject H0**Contingency Analysis(From Figure 14-9)**Test Statistic: Since 76.188 > 3.841, reject H0**Contingency Analysis**EXPECTED CELL FREQUENCIES**• Chi-Square Goodness-of-Fit test**• Contingency Table Key Terms