Question 2

A chi-square test for homogeneity is used to determine whether subgroups of a population have the same distribution.

A chi-square test for homogeneity specifically assesses if the distribution of a categorical variable is the same across different subgroups in a population.

A) Whether the paired mean differences for two populations are significantly different

This option refers to a t-test for paired samples, which is used to compare the means of two related groups. It is not relevant to the chi-square test for homogeneity, which focuses on categorical data rather than mean differences.

B) Whether there is a linear association between two quantitative variables

This option describes a correlation or regression analysis, used to assess relationships between quantitative variables. The chi-square test for homogeneity does not examine linear associations but rather categorical distributions across subgroups.

C) Whether subgroups of a population have the same distribution

This is the correct answer, as the chi-square test for homogeneity is designed to determine if different subgroups (or categories) within a population exhibit the same distribution for a categorical variable. This test is essential for understanding how variables may differ across groups.

D) Whether the categories for one qualitative variable differ significantly in their frequencies

This option is related to the chi-square test for independence rather than homogeneity. While both tests involve categorical data, the test for homogeneity specifically compares distributions across multiple groups rather than just evaluating frequency differences within a single group.

Conclusion

The chi-square test for homogeneity is specifically tailored to analyze whether different subgroups of a population share the same distribution of a categorical variable, making option C the definitive correct answer. Other options either pertain to different statistical tests or do not accurately describe the purpose of the chi-square test for homogeneity, reinforcing why they are not suitable choices.