Find the rejection region for a test of independence of two classifications where the contingency table contains $r = 2$ rows and $c = 4$ columns and $\alpha = .10$.
A) $\chi ^ { 2 } 22.307$
B) $\chi ^ { 2 } 15.507$
C) $\chi ^ { 2 } 6.251$
D) $\chi ^ { 2 } 13.362$

Question

Find the rejection region for a test of independence of two classifications where the contingency table contains $r = 2$ rows and $c = 4$ columns and $\alpha = .10$.
A) $\chi ^ { 2 } > 22.307$
B) $\chi ^ { 2 } > 15.507$
C) $\chi ^ { 2 } > 6.251$
D) $\chi ^ { 2 } > 13.362$

Quizplus · Accepted Answer

The degrees of freedom for a chi-square test of independence is calculated as $(r - 1) \times (c - 1)$. Here, $r = 2$ and $c = 4$, so the degrees of freedom is $(2 - 1) \times (4 - 1) = 3$. For a significance level of $\alpha = .10$ and 3 degrees of freedom, the critical value from the chi-square distribution table is $6.251$. Therefore, the rejection region is $\chi ^ { 2 } > 6.251$.

Find the Rejection Region for a Test of Independence of Two