Resolved: dependent samples with known population variance
You have explained dependent samples with two use cases Before and After and Cause and Effect, but is it further separated by population variance Known or Unknown like below. If yes, are we going to use z-stat for known population variance even when sample size is less than 30..
1. Before & After - population variance Known
2. Before & After - Population variance unknown
That is correct, as long as we have known population variance, the z-statistic is applicable. Otherwise, we use the t-statistic.
If you didn't noticed, the calculation for dependent samples actually follow that of the one-sample test. Only this time, we use the difference between Before and After data as our singe variable d.