Chapter 7.2, Problem 31E

To determine

Find the expected count and the contribution to the chi-square statistic for the cell (Group 3, Yes).

Answer to Problem 31E

The expected count and the contribution to the chi-square statistic for the cell (Group 3, Yes) are 65 and 0.754, respectively.

Explanation of Solution

From the given table, row and column totals for the cell (Group 3, Yes) (=72) are 100 and 260, respectively. The grand total, n, is 400.

The expected count can be calculated as follows:

$\begin{array}{c}\text{Expected count}=\frac{\left(\text{Group 3 row total}\right)\left(\text{Yes column total}\right)}{n}\\ =\frac{\left(100\right)\left(260\right)}{400}\\ =\underset{\_}{65}\end{array}$

The contribution to the chi-square statistic can be calculated as follows:

$\begin{array}{c}{\chi }^2=\frac{{\left(\text{Observed}-\text{Expected}\right)}^2}{\text{Expected}}\\ =\frac{{\left(72-65\right)}^2}{65}\\ \approx \underset{\_}{0.754}\end{array}$