In a chi-square test for independence, the null hypothesis states what?

In a chi-square test for independence, the null hypothesis states what?

• A. The two categorical variables are dependent.
• B. The variables have equal distributions.
• C. The two categorical variables are independent.
• D. The variables share the same mean.

Answer: (C)

In a chi-square test for independence, the null hypothesis says there is no association between two categorical variables; they are independent. This means the distribution of one variable does not depend on the level of the other variable, and the joint probabilities factor into the product of the marginals. In practice, you compute expected counts in each cell as (row total × column total) / grand total under this independence assumption. If the observed counts differ substantially from these expected counts, you have evidence against independence. This is why the statement that the two categorical variables are independent is the correct choice. The idea that they are dependent would be the alternative hypothesis, and phrases about equal distributions or shared means aren’t the right framing for a chi-square test with categorical data.

In a chi-square test for independence, the null hypothesis says there is no association between two categorical variables; they are independent. This means the distribution of one variable does not depend on the level of the other variable, and the joint probabilities factor into the product of the marginals. In practice, you compute expected counts in each cell as (row total × column total) / grand total under this independence assumption. If the observed counts differ substantially from these expected counts, you have evidence against independence.

This is why the statement that the two categorical variables are independent is the correct choice. The idea that they are dependent would be the alternative hypothesis, and phrases about equal distributions or shared means aren’t the right framing for a chi-square test with categorical data.