Which of the following accurately describes the $\chi ²$ test for independence?

• A. It is a statistical test used to determine whether there is a significant association between two categorical variables in a contingency table.
• B. It is a test used to compare the means of two independent samples.
• C. It is a test used to assess the normality of a distribution.
• D. It is a test used to estimate the population variance from a sample.

Answer: (A)

Verified step by step guidance

1. Understand that the chi-square test for independence is used to analyze the relationship between two categorical variables organized in a contingency table.
2. Recognize that this test evaluates whether the observed frequencies in each category differ significantly from the frequencies expected if the variables were independent.
3. Recall that the test statistic is calculated using the formula: \(\chi^2 = \sum \frac{(O - E)^2}{E}\), where \(O\) represents observed frequencies and \(E\) represents expected frequencies under the assumption of independence.
4. Note that the chi-square test for independence is not used for comparing means, assessing normality, or estimating variance; those are different statistical tests with distinct purposes.
5. Conclude that the correct description of the chi-square test for independence is that it determines whether there is a significant association between two categorical variables in a contingency table.