A pollster collects data on gender (male, female) and car choice (American, Asian, European) to examine whether gender is related to car choice. Which test is appropriate?

A pollster collects data on gender (male, female) and car choice (American, Asian, European) to examine whether gender is related to car choice. Which test is appropriate?

• A. Chi-square test of independence with 2 degrees of freedom
• B. Chi-square test of homogeneity
• C. Fisher's exact test
• D. Two-proportion z-test

Answer: (A)

This question is about whether two categorical variables are related. Gender has 2 categories and car choice has 3 categories, giving a 2-by-3 contingency table. To test if gender and car preference are associated, use the chi-square test of independence. It compares observed counts in each cell to what would be expected if the variables were independent, and its degrees of freedom are (2−1)×(3−1) = 2, which matches the given 2 degrees of freedom. Why not the others: the chi-square test of homogeneity would be used when comparing distributions across different populations rather than testing a relationship between two variables in one population. Fisher's exact test is an exact alternative typically used for small samples, especially 2-by-2 tables; for a 2-by-3 table it’s less standard unless sample sizes are very small. The two-proportion z-test looks at a single proportion difference, not the entire cross-tabulation across multiple categories, so it isn’t appropriate for this scenario.

This question is about whether two categorical variables are related. Gender has 2 categories and car choice has 3 categories, giving a 2-by-3 contingency table. To test if gender and car preference are associated, use the chi-square test of independence. It compares observed counts in each cell to what would be expected if the variables were independent, and its degrees of freedom are (2−1)×(3−1) = 2, which matches the given 2 degrees of freedom.

Why not the others: the chi-square test of homogeneity would be used when comparing distributions across different populations rather than testing a relationship between two variables in one population. Fisher's exact test is an exact alternative typically used for small samples, especially 2-by-2 tables; for a 2-by-3 table it’s less standard unless sample sizes are very small. The two-proportion z-test looks at a single proportion difference, not the entire cross-tabulation across multiple categories, so it isn’t appropriate for this scenario.