Question

Give a two-way table and specify a particular cell for that table. In each case find the expected count for that cell and the contribution to the chi- square statistic for that cell. \((\mathrm{B}, \mathrm{E})\) cell $$ \begin{array}{l|rrrr|r} \hline & \text { D } & \text { E } & \text { F } & \text { G } & \text { Total } \\ \hline \text { A } & 39 & 34 & 43 & 34 & 150 \\ \text { B } & 78 & 89 & 70 & 93 & 330 \\ \text { C } & 23 & 37 & 27 & 33 & 120 \\ \hline \text { Total } & 140 & 160 & 140 & 160 & 600 \\ \hline \end{array} $$

Short answer

The expected count for cell (B, E) is 88 and its contribution to the chi-square statistic is 0.0114.

Step-by-step solution

Calculate the Expected Count

To calculate the expected count for cell (B, E), multiply the total for row B (330) by the total for column E (160), then divide by the overall total (600). So, the expected count \(E(B,E) = \frac{{330 \times 160}}{{600}} = 88\).

Calculate the Contribution to the Chi-Square Statistic

To calculate the contribution to the chi-square statistic for cell (B, E), first find the difference between the observed count (O = 89) and the expected count (E = 88). Then square this difference and divide by the expected count. So, the Chi-square contribution \(\chi^2(B,E) = \frac{{(O - E)^2}}{{E}} = \frac{{(89 - 88)^2}}{{88}} = 0.0114\).