Do the null and alternative hypotheses have to be complements? In
other words, can one set up a problem like:
H0: d = 0
H1: d <= 0
when d can take positive values? Or must one couch the problem as:
H0: d=0
H1: d<0 OR d>0
If you can go with the one-tailed test, does choosing it imply a
different Type II loss function than in the two-tailed test? Are there
any other hidden assumptions underlying the choice of a one-tailed test
in this context?
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