In the context of a chi-square test for independence, what does a large value of the $\chi 2^{}$ statistic indicate about the relationship between the two categorical variables being tested?

• A. The sample size is too small to draw any conclusions.
• B. There is strong evidence that the two variables are not independent.
• C. The expected frequencies are equal to the observed frequencies.
• D. There is strong evidence that the two variables are independent.

Answer: (B)

Verified step by step guidance

1. Recall that the chi-square test for independence is used to determine whether there is a significant association between two categorical variables.
2. Understand that the chi-square statistic measures the difference between the observed frequencies and the expected frequencies under the assumption that the variables are independent.
3. A large chi-square statistic means that the observed frequencies differ greatly from the expected frequencies, suggesting that the assumption of independence may not hold.
4. Therefore, a large value of the chi-square statistic provides strong evidence against the null hypothesis of independence, indicating that the two variables are likely related.
5. In summary, a large chi-square value suggests that the two categorical variables are not independent, meaning there is an association between them.