I find z for means quite a bit more accessible to
students. Positively, we can say up front that we are
going to explore the reasoning of inference in an overly
simple setting. Remember, an exactly normal population
and a true simple random sample (SRS) are as unrealistic
as known . All the issues of practice—robustness
against lack of normality, application when the data
aren’t an SRS—are put off until, with the reasoning
already in hand, we discuss the practically useful
t procedures. This separation of initial reasoning from
messier practice works well.