Question

Explain the difference between situations that would lead to a chi-square goodness-of-fit test and those that would lead to a chi-square test of homogeneity.

Short answer

A chi-square goodness-of-fit test is used to compare a single observed distribution to an expected distribution, such as testing if the distribution of colors in a bag of candy matches the claimed distribution. A chi-square test of homogeneity is used when comparing distributions across different groups, like testing if there's a difference in ice cream flavor preference across age groups.

Step-by-step solution

Situation for chi-square goodness-of-fit test

The chi-square goodness-of-fit test is utilized when testing whether a single categorical variable follows a hypothesized distribution within the population. For example, it might be used to attest if the distribution of colors in a bag of candy matches the hypothetical distribution presented by the manufacturer.

Situation for chi-square test of homogeneity

The chi-square test of homogeneity is used in a different type of situation. This test is used when comparing the distribution of a categorical variable for different populations or groups. It might be used, for instance, to test if there is a difference in the distribution of favorite ice cream flavors between different age groups.

Summary of differences between the two situations

In general, the chi-square goodness-of-fit test is used when testing the distribution of a single variable against a hypothetical expectation, while the chi-square test of homogeneity is used when comparing distributions across different groups or populations.