Question

A scientist was interested in studying if students' religious beliefs change as they go through college. One hundred randomly selected students were asked before they entered college if they would consider themselves religious, yes or no. Four years later, the same one hundred students were asked if they would consider themselves religious, yes or no. The scientist decided to perform McNemar's test. The data is below.

After College, Yes After College, No
Before College, Yes 55 23
Before College, No 11 11

Are the assumptions met for McNemar's test?

A. Yes, n is greater than 30.

B. No, n is not greater than 30.

C. Yes, n is greater than 15.

D. Yes, YN + NY is greater than or equal to 30.

E. No, YN + NY is not greater than or equal to 30.

Answer 1

The assumptions for McNemar's test are that the data is paired, the responses are dichotomous, there is a dependent relationship between the measurements, the sample size is large enough, and the paired responses are mutually exclusive. Therefore, the correct answer is E. No, YN + NY is not greater than or equal to 30.

Step-by-step explanation:

McNemar's test is used for comparing paired proportions, especially in situations where the data is dichotomous (yes/no in this case). The assumptions for McNemar's test include:

Binary Response: The data must be dichotomous, with each subject having only two possible responses.

Matched Pairs: The responses must be collected in pairs, and the subjects must be matched.

Independent Pairs: The pairs must be independent of each other.

Large Sample Size: A common rule of thumb is that the total number of discordant pairs (pairs where one member changed response) should be greater than or equal to 25.

Looking at the options:

A. No information is provided about the sample size (n) being greater than 30.

B. This is a general statement, not specific to McNemar's test.

C. McNemar's test doesn't have a strict requirement for n being greater than 15.

D. This is a correct statement. McNemar's test considers the sum of discordant pairs (YN and NY), and this sum should ideally be larger for the test to be reliable.

E. This is the correct answer. It specifically mentions the sum of discordant pairs, and McNemar's test may not be suitable if this sum is too small.

Therefore, the correct answer is E. No, YN + NY is not greater than or equal to 30.