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. Party Approve Disapprove No Opinion $$\begin{array} { l | c c c }
& { \text { Opinion } } \
\hline \text { Party } & \text { Approve } & \text { Disapprove } & \text { No Opinion } \
\text { Republican } & 42 & 20 & 14 \
\text { Democrat } & 50 & 24 & 18 \
\text { Independent } & 10 & 16 & 6
\end{array}$$ Find the chi-square test statistic χ2 used to test the claim of independence.
A) 8.030
B) 11.765
C) 7.662
D) 9.483

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. Party Approve Disapprove No Opinion $$\begin{array} { l | c c c } 
& { \text { Opinion } } \
\hline \text { Party } & \text { Approve } & \text { Disapprove } & \text { No Opinion } \
\text { Republican } & 42 & 20 & 14 \
\text { Democrat } & 50 & 24 & 18 \
\text { Independent } & 10 & 16 & 6
\end{array}$$ Find the chi-square test statistic χ2 used to test the claim of independence.
A) 8.030
B) 11.765
C) 7.662
D) 9.483

Quizplus · Accepted Answer

The chi-square test statistic is calculated as:$$\chi^2 = \sum \frac{(O - E)^2}{E}$$where O is the observed frequency and E is the expected frequency.The expected frequency is calculated as:$$E = \frac{(	ext{row total})(	ext{column total})}{	ext{grand total}}$$For example, the expected frequency for the cell in the first row and first column is:$$E = \frac{(42 + 20 + 14)(42 + 50 + 10)}{200} = 35$$The chi-square test statistic is then calculated as:$$\chi^2 = \frac{(42 - 35)^2}{35} + \frac{(20 - 28)^2}{28} + \frac{(14 - 17)^2}{17} + \frac{(50 - 35)^2}{35} + \frac{(24 - 28)^2}{28} + \frac{(18 - 17)^2}{17} + \frac{(10 - 14)^2}{14} + \frac{(16 - 11)^2}{11} + \frac{(6 - 9)^2}{9} = 8.030$$Therefore, the chi-square test statistic is 8.030.

The Contingency Table Below Shows the Results of a Random