Question

Could mud wrestling be the cause of a rash contracted by University of Washington students? Two physicians at the university’s student health center wondered about this when one male and six female students complained of rashes after participating in a mud-wrestling event. Questionnaires were sent to a random sample of students who participated in the event. The results, by gender, are summarized in the following table.

Here is some computer output for the preceding table. The output includes the observed counts, the expected counts, and the chi-square statistic.

The cell that contributes most to the chi-square statistic is

a. men who developed a rash.

b. men who did not develop a rash.

c. women who developed a rash.

d. women who did not develop a rash.

e. both (a) and (d).

Short answer

The answer is option (c) women who developed a rash.

Step-by-step solution

Given information

The given data is

Explanation

A study was done to see if mud wrestling could be the cause of a rash that University of Washington students had contracted. As a result, we must first determine the difference between the observed and predicted frequency as follows:

Men who got a rash included:

$$\begin{gathered} |O-E|=|12-16.22| \\ =4.22 \end{gathered}$$

Men who did not develop a rash:

$$\begin{gathered} |O-E|=|38-33.78| \\ =4.22 \end{gathered}$$

Women who got a rash included:

$$\begin{gathered} |O-E|=|12-7.78| \\ =4.22 \end{gathered}$$

Women who did not develop a rash:

$$\begin{gathered} |O-E|=|12-16.22| \\ =4.22 \end{gathered}$$

So, if all four cells have the same difference, the cell that contributed the most is the one with the lowest predicted value. Women who acquired a rash have the lowest anticipated value ($7.78$), and so they contribute the most to the chi-square statistic. As a result, option (c) is the proper choice.