Chapter 12: Q. AP4.19 (page 830)

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.
From the chi-square test performed in this study, we may conclude that
a. there is convincing evidence of an association between the gender of an individual participating in the event and the development of a rash.
b. mud wrestling causes a rash, especially for women.
c. there is absolutely no evidence of any relationship between the gender of an individual participating in the event and the subsequent development of a rash.
d. development of a rash is a real possibility if you participate in mud wrestling, especially if you do so regularly.
e. the gender of the individual participating in the event and the development of a rash are independent.

Short Answer

Expert verified

The correct answer is option (a) There is convincing evidence of an association between the gender of an individual participating in the event and the development of 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 of the possibilities, we may conclude that

Option (a): This can be determined because the chi-square test's null hypothesis claims that there is no correlation, whereas the alternative hypothesis states that there is.

Option (b): This can't be inferred because a chi-square test can only show association, not causation.

Option (c): This cannot be concluded because a sample always contains evidence.

Option (d): We can't draw any conclusions because we don't have any data on how often people participate in mud wrestling.

Option (e): This can't be concluded because the chi-square test just shows whether there's a link or not; it doesn't tell us if there's a link or not.

As a result, option (a) is the proper choice.