When is a chi-square goodness-of-fit test appropriate?

• A. It tests the association between two categorical variables in a contingency table.
• B. It compares observed categorical frequencies to expected frequencies under a specified distribution.
• C. It estimates population means.
• D. It measures the strength of a relationship between two variables.

Answer: (B)

Goodness-of-fit chi-square is used when you want to know if the observed frequencies in categorical categories match what would be expected if the data followed a specific distribution. You compare what you actually saw in each category to what you would expect under your hypothesis (for example, equal frequencies across categories or a known set of proportions). The test sums (O − E)² / E across all categories to produce a statistic that, under the null hypothesis, follows a chi-square distribution. If the observed counts differ from the expected counts more than would be due to chance, you reject the hypothesis that the data follow the specified distribution. This approach is about how well data fit a distribution, not about whether two variables are related (that would be a chi-square test of independence) or about estimating population means or the strength of a relationship.