The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. $$\begin{array} { l | c c c }
& { \text { Opinion } } \
\hline \text { Party } & \text { Approve } & \text { Disapprove } & \text { No Opinion } \
\text { Republican } & 42 & 20 & 14 \
\text { Democrat } & 50 & 24 & 18 \
\text { Independent } & 10 & 16 & 6
\end{array}$$ Find the critical value χ $$\chi _ { 0 } ^ { 2 }$$ , to test the claim of independence using α = 0.05.
A)9.488
B)7.779
C)11.143
D)13.277

Question

The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. $$\begin{array} { l | c c c } 
& { \text { Opinion } } \
\hline \text { Party } & \text { Approve } & \text { Disapprove } & \text { No Opinion } \
\text { Republican } & 42 & 20 & 14 \
\text { Democrat } & 50 & 24 & 18 \
\text { Independent } & 10 & 16 & 6
\end{array}$$ Find the critical value χ $$\chi _ { 0 } ^ { 2 }$$ , to test the claim of independence using α = 0.05.
A)9.488
B)7.779
C)11.143
D)13.277

Quizplus · Accepted Answer

The degrees of freedom for a chi-square test of independence are calculated as (r - 1)(c - 1), where r is the number of rows and c is the number of columns in the contingency table. Here, r = 3 (Republican, Democrat, Independent) and c = 3 (Approve, Disapprove, No Opinion), so the degrees of freedom are (3 - 1)(3 - 1) = 2 * 2 = 4. For a chi-square test with 4 degrees of freedom and a significance level of α = 0.05, the critical value is 9.488.

The Contingency Table Below Shows the Results of a Random