Question

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).

Question refers to the following situation:

Could mud wrestling be the cause of a rash contracted by University of Washington students? Two physicians at the University of Washington 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.

Some Minitab output for the previous table is given below. The output includes the observed counts, the expected counts, and the chi-square statistic.

Short answer

Option (c) is correct. Women who developed a rash.

Step-by-step solution

Given information

We have been given that the data of the random samples of participants (men and women) participated in mud wrestling event. These samples were collected when one male and six female students complained of rashes after participating in a mud-wrestling event. Data is depicted in the tables given in question.

We need to find the cell that contributes most to the chi-square statistics.

Simplify

Firstly, find the difference between an observed frequency and an expected frequency for men and women:

Women who developed a rash:

$\left|Observed-Expected\right|=\left|12-7.78\right|=4.22$

Women who did not develop a rash:

$\left|Observed-Expected\right|=\left|12-16.22\right|=4.22$

Men who developed a rash:

$\left|Observed-Expected\right|=\left|12-16.22\right|=4.22$

Men who did not develop a rash:

$\left|Observed-Expected\right|=\left|38-33.78\right|=4.22$

We have observed that all the four cells have the same difference of observed and expected frequency. So, that's why, the cell which has the lowest expected value contributed the most.

The lowest expected value is for women who developed a rash i.e. $7.78$.

So, the women who developed a rash contribute the most to the chi-square statistic.