Chapter 12, Problem AP4.18CPT

To determine

To find out the cell that contribute most to the chi-square statistic is what.

Answer to Problem AP4.18CPT

Option (c) is the correct option.

Explanation of Solution

In the question, a study was conducted to find out could the mud wrestling be the cause of a rash contracted by University of Washington students. Thus, we have to first find out the difference between the observed and the expected frequency as:

Men who developed rash:

  $\begin{array}{l}\left|O-E\right|=\left|12-16.22\right|\\ =4.22\end{array}$

Men who developed no rash:

  $\begin{array}{l}\left|O-E\right|=\left|38-33.78\right|\\ =4.22\end{array}$

Women who developed rash:

  $\begin{array}{l}\left|O-E\right|=\left|12-7.78\right|\\ =4.22\end{array}$

Women who developed no rash:

  $\begin{array}{l}\left|O-E\right|=\left|12-16.22\right|\\ =4.22\end{array}$

Thus, we note that all four cells have an equal difference, then the cell that contributed the most is the cell that has the lowest expected value. The lowest expected value is $7.78$ for women who developed a rash and thus women who developed a rash contribute the most to the chi-square statistic. Thus, option (c) is the correct option.