Question

A scientist was interested in determining if students eating habits change as they go through college. One hundred randomly selected students were asked before they entered college if they would consider themselves vegetarians, yes or no. Four years later, the same one hundred students were asked if they would consider themselves vegetarians, yes or no. The scientist decided to perform McNemar's test. The data is below. Are the assumptions met for McNemar's test?

After College
Before College Yes NO
Yes 20 10
No 5 165
A. Yes, n is greater than 15.
B. No, YN + NY is not greater than 30.
C. Yes, YN + NY is greater than 30.
D. Yes, n is greater than 30.
E. No, n is not greater than or equal to 30.

Answer 1

It is to be noted that the assumptions were not met for McNemar's test. Hence the correct answer is Option E. No, n is not greater than or equal to 30.

McNemar's test is typically appropriate when the study involves paired categorical data and the sample size is sufficiently large. The key assumption is that the number of discordant pairs (where one individual changes and the other does not) is reasonably large.

In this case, the discordant pairs are those who switched from "Yes" before college to "No" after college or vice versa. In the provided data:

- YN = 10 (students who were vegetarians before but not after)

- NY = 5 (students who were not vegetarians before but were after)

The sum YN + NY = 10 + 5 = 15, which is less than 30.

Therefore, the assumption for McNemar's test (that the number of discordant pairs is greater than 30) is not met.

The correct answer is: E. No, n is not greater than or equal to 30.