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 affiliations. Assuming the row and column classifications are independent, find an estimate for the expected cell count $E _ { 22 }$ . $$\begin{array} { l | c c c }
&{ \text { Opinion } } \
\hline \text { Party } & \text { Approve } & \text { Disapprove } & \text { No Opinion } \
\text { Republican } & 42 & 20 & 14 \
\text { Democrat } & 50 & 24 & 18 \
\text { Independent } & 10 & 16 & 6
\end{array}$$
A) 27.6
B) 22.8
C) 46.92
D) 17.48

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 affiliations. Assuming the row and column classifications are independent, find an estimate for the expected cell count $E _ { 22 }$ . $$\begin{array} { l | c c c } 
&{ \text { Opinion } } \
\hline \text { Party } & \text { Approve } & \text { Disapprove } & \text { No Opinion } \
\text { Republican } & 42 & 20 & 14 \
\text { Democrat } & 50 & 24 & 18 \
\text { Independent } & 10 & 16 & 6
\end{array}$$
A) 27.6
B) 22.8
C) 46.92
D) 17.48

Quizplus · Accepted Answer

The expected cell count is calculated by multiplying the row total by the column total and dividing by the grand total. For cell $E _ { 22 }$, the row total is 24, the column total is 40, and the grand total is 200. Therefore, the expected cell count is $E _ { 22 } = ( 24 \times 40 ) / 200 = 22.8$.

The Contingency Table Below Shows the Results of a Random E22E _ { 22 }E22​

The Contingency Table Below Shows the Results of a Random $E _ { 22 }$