Question

How would you respond to a colleague who indicated he was planning to use a z-test to determine whether men or women were more likely to have joined a study group? What explanation would you give to help your colleague understand why you responded the way you did?

Answer 1

Using a z test for determining whether men or women were more likely to have joined a study group is not good statistical test. In this case, it is clear that we will have 2 independent samples, one for men and one for women. We have no information about the population distribution for the sampled data.

So, I will not suggest to use z test for this statistical test because two independent sample t test is more appropriate in this case as compared to the z test. Population is unknown, so t test is more useful than z test.

So, two independent samples t test is useful in this case because we have to independent samples, one for men and one for women. So, using z test for two independent samples is not efficient. Two independent samples t test is useful in this case because we are comparing two samples where population parameters are unknown.