Question

# Find the expected count and the contribution to the chi-square statistic for the (Group 1, Yes) cell in the two-way table below. begin{array}{|c|c|c|}

Two-way tables
Find the expected count and the contribution to the chi-square statistic for the (Group 1, Yes) cell in the two-way table below.
$$\begin{array}{|c|c|c|}\hline&\text{Yes}&\text{No}&\text{Total}\\\hline\text{Group 1} &710 & 277 & 987\\ \hline\text{Group 2}& 1175 & 323&1498\\\hline \ \text{Total}&1885&600&2485 \\ \hline \end{array}$$
Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.
Expected count=?
contribution to the chi-square statistic=?

2020-12-15

Step 1 Given information $$\begin{array}{|c|c|c|}\hline&\text{Yes}&\text{No}&\text{Total}\\\hline\text{Group 1} &710 & 277 & 987\\ \hline\text{Group 2}& 1175 & 323&1498\\\hline \ \text{Total}&1885&600&2485 \\ \hline \end{array}$$

Step 2 Expected value is given by

$$\begin{array}{|c|c|c|}\hline&\text{Yes}&\text{No}\\\hline\text{Group 1} & \frac{1885\times987}{2485}=748.7 & \frac{600\times987}{2485}=238.3 \\ \hline\text{Group 2}&\frac{1885\times1498}{2485}=1136.3 & \frac{600\times1498}{2485}=361.7\\\hline\end{array}$$

Test statistic $$x^2=\sum \frac{(O_i-E_i)^2}{E_i}$$
$$x^2=\frac{(710-748.7)^2}{748.7}+\frac{(277-238.3)^2}{238.3}+\frac{(1175-1136.3)^2}{1136.3}+\frac{(323-361.7)^2}{361.7}=13.737$$