In a chi-squared test of independence, the value of the test statistic was $x ^ { 2 } =$ 15.652, and the critical value at $\alpha = 0.025$ was 11.1433. Thus we must reject the null hypothesis at $\alpha = 0.025$ .

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Since the test statistic (15.652) is greater than the critical value (11.1433) at $\alpha = 0.025$, we reject the null hypothesis, indicating a significant association between the variables tested.

In a Chi-Squared Test of Independence, the Value of the Test