CDROM Chapter 14 GoodnessofFit Tests and Contingency Analysis

Chapter 14 - Chapter Outcomes After studying the material in this chapter, you should

Chi-Square Goodness-of-Fit Test CHI-SQUARE GOODNESS OF FIT TEST STATISTIC where: k = Number of

Chi-Square Goodness-of-Fit Test (Vista Health Guard Example) H 0: Patient demand is evenly spread

Chi-Square Goodness-of-Fit Test (Figure 14 -3)

Chi-Square Goodness-of-Fit Test (Figure 14 -3) f( 2) d. f. = k - 1

Chi-Square Goodness-of-Fit Test (Figure 14 -3) Since 3, 302. 7 > 12. 592, reject

Contingency Analysis A contingency table is a table used to classify sample observations according

Contingency Analysis CHI-SQUARE CONTINGENCY TEST STATISTIC where: oij = Observed frequency in cell (i,

Contingency Analysis (From Figure 14 -9) H 0: Gender of yearbook editor is independent

Contingency Analysis (From Figure 14 -9) f( 2) d. f. = (r - 1)(c

Contingency Analysis (From Figure 14 -9) Test Statistic: Since 76. 188 > 3. 841,

Contingency Analysis EXPECTED CELL FREQUENCIES

Key Terms • Chi-Square Goodness-of-Fit test • Contingency Table

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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) H 0: 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)

Chi-Square Goodness-of-Fit Test (Figure 14 -3) f( 2) d. f. = k - 1 = 7 - 1 = 6 Rejection Region = 0. 05 Decision Rule: If 2 > 12. 592, reject H 0 Otherwise, do not reject H 0 2 = 12. 592 2

Chi-Square Goodness-of-Fit Test (Figure 14 -3) Since 3, 302. 7 > 12. 592, reject H 0

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) H 0: 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 Male Actual = 14 Expected = 39. 98 Actual = 43 Expected = 17. 02 Female Actual = 141 Expected = 115. 02 Actual = 23 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 = 3. 841 Decision Rule: If 2 > 3. 841, reject H 0 Otherwise, do not reject H 0 2

Contingency Analysis (From Figure 14 -9) Test Statistic: Since 76. 188 > 3. 841, reject H 0

Contingency Analysis EXPECTED CELL FREQUENCIES

Key Terms • Chi-Square Goodness-of-Fit test • Contingency Table