If H0 is retained
NO definite statement about u can be made.
If H0 is rejected
then an inference regarding the direction of difference between true U and U0 can be made.
However - "statistical significance"
tells us nothing about the size of effect.
However - "statistical significance" tells us nothing about the size of effect.
That is, the size of the test statistic (e.g. t or Z) does not convey information about the size or importance of the difference between true u and u0.
So a large t statistic
does not necessarily imply that the detected effect is large or functionally important
By contrast, confidence intervals do convey
information about size of effect
each case in one sample corresponds to a particular case in other sample eg repeated measures design
test of dependent means (=correlated means)
cases in each sample are completely independent eg between-group design
test of independent means