>>11342457The problem I see is better ilustraded by the use of Central Limit Theorem. If you don't check any of the theorems proof (there's a few of them), you could misuse the theorem hard and it is one of the symptoms of bad usage of statistics.
The proofs should be studied at least once, so one could understand what is happening. No one is expected to come up with a new variation of the proof, but at least stick with the hypothesis and respect the line of thought that backs the theorem.
