Can a hypothesis test yield a statistically significant (say p<=0.05), yet practically meaningless result? Give an example of how this might happen.

You are asking if statistical significance may not be practically significant. Although I cannot cite the study, it found that, as you go up the executive ladder for business, people are taller. Does this justify promoting taller applicants, especially since the differences between levels are mere fractions of an inch?

Can this help you think of your own example?