But maybe the BMIs of all the participants changed during the four-week period. We can calculate the

Question:

But maybe the BMIs of all the participants changed during the four-week period. We can calculate the change in BMI for each participant in the study, and then compare the mean change for the 41 maids in the informed group with the mean change for the 34 in the uninformed group. Here is a display (Informed = 1 means informed, Informed = 0 means uninformed):

Which of these inference methods would you use to tell whether informing the maids made a difference in their BMIs?
a) See if the boxes in the boxplot overlap. The difference is significant if they don’t.
b) Find a confidence interval for the paired changes in BMI for each group. If the confidence intervals don’t overlap, then they are different.
c) Perform a two-sample t-test comparing whether the mean changes for the two groups are equal.
d) Use a x²test of homogeneity.
e) Use a two-sample z-test for the proportions that gained weight in each group.