A data analyst is performing a chi-square test of independence on a contingency table of customer satisfaction (satisfied vs. dissatisfied) and product type (A, B, C). The test yields a p-value of 0.04 with α = 0.05. What is the correct conclusion?
With p = 0.04 below the α = 0.05 threshold, the null hypothesis of independence is rejected, so satisfaction and product type are statistically associated. The chi-square test of independence detects whether the two categorical variables' observed cell frequencies deviate from those expected under independence.
Why this answer
With a p-value of 0.04 and α = 0.05, the p-value is less than the significance level, so we reject the null hypothesis of independence. This means there is statistically significant evidence of an association between customer satisfaction and product type. The correct conclusion is that a significant association exists.
Exam trap
DA0-002 often tests the interpretation of p-values versus α, and candidates frequently confuse 'fail to reject' with 'accept the null' or misinterpret a significant result as proving causation rather than association.
How to eliminate wrong answers
Option A is wrong because it states there is no evidence of association, which would be the conclusion if we failed to reject the null hypothesis (p ≥ α). Option C is wrong because the question does not provide information about expected counts; while chi-square requires expected counts ≥ 5 in each cell, the p-value alone does not indicate invalidity. Option D is wrong because it states the variables are independent, which is the null hypothesis we rejected.