Which scenario best illustrates using a chi-square test of independence?

• A. Examining whether gender is related to smoking status.
• B. Testing whether a sample mean differs from a known value.
• C. Testing whether data are normally distributed.
• D. Estimating a population proportion.

Answer: (A)

Chi-square test of independence asks whether two categorical variables are related or independent. It uses observed counts in each combination of categories and compares them to what would be expected if there were no relationship between the variables. Here, gender and smoking status are both categorical, so you can lay out a contingency table (for example, male vs female crossed with smoker vs non-smoker) and test whether the distribution of smoking status differs by gender. If there’s no association, the pattern of smoking should be similar across genders, leading to a small chi-square value.

The other scenarios don’t fit this test: comparing a sample mean to a known value is about a mean difference, not relationships between categorical variables; checking if data are normally distributed is about distribution shape rather than relationships between categories; estimating a population proportion concerns a single proportion rather than the relationship between two variables.