To test whether overtime occurrences are equally likely across NBA, NFL, NHL, and MLB, which inference method should be used?

To test whether overtime occurrences are equally likely across NBA, NFL, NHL, and MLB, which inference method should be used?

• A. ANOVA
• B. Fisher's exact test
• C. Chi-square test of homogeneity with 3 degrees of freedom
• D. Z-test for proportions

Answer: (C)

The main idea is to compare how a binary outcome (overtime yes or no) occurs across four leagues to see if the rates are the same. The appropriate method is the chi-square test of homogeneity, which uses a contingency table with leagues as rows and overtime occurrence as columns. The null hypothesis is that the overtime proportion is identical across all leagues. The test checks how observed counts differ from expected counts under that common distribution, taking into account the group sizes. The degrees of freedom for this setup are (number of leagues − 1) × (number of outcomes − 1) = (4 − 1) × (2 − 1) = 3, matching the stated option. ANOVA is for comparing means of a continuous variable, not a binary outcome; a Z-test for proportions compares two groups; Fisher’s exact test is typically for small samples in 2×2 tables.

The main idea is to compare how a binary outcome (overtime yes or no) occurs across four leagues to see if the rates are the same. The appropriate method is the chi-square test of homogeneity, which uses a contingency table with leagues as rows and overtime occurrence as columns. The null hypothesis is that the overtime proportion is identical across all leagues. The test checks how observed counts differ from expected counts under that common distribution, taking into account the group sizes. The degrees of freedom for this setup are (number of leagues − 1) × (number of outcomes − 1) = (4 − 1) × (2 − 1) = 3, matching the stated option. ANOVA is for comparing means of a continuous variable, not a binary outcome; a Z-test for proportions compares two groups; Fisher’s exact test is typically for small samples in 2×2 tables.