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. what is the test statistic? after college before college yes no yes 55 23 no 11 11 group of answer choices 1.96 or -1.96 1.35 or -1.35 55 or -55 32 or -32 2.05 or -2.05

Answer 1

To perform McNemar's test, we need to find the number of discordant pairs, i.e., the pairs of individuals who change their response from before to after college. In this case, there are 23 students who said "yes" before college but "no" after college, and 11 students who said "no" before college but "yes" after college. Therefore, there are 23 discordant pairs.

The test statistic for McNemar's test is calculated as:

z = (|b-c| - 1) / √(b+c)

where b is the number of discordant pairs who responded "yes" before college, and c is the number of discordant pairs who responded "no" before college.

In this case, b = 23 and c = 11, so:

z = (|23-11| - 1) / √(23+11)

z = 1.96

Therefore, the test statistic is 1.96