A human is walking down a street late at night when they see another human on their hands and knees searching the ground around a lamppost. The searcher explains that they lost their wedding ring, so the passerby helps them look. After a while, the passerby asks, “are you sure this is where you dropped it?”. The other human says, “no, I dropped it over there. But this is where the light is!”.
We do powerful tests using the normality assumption because the assumption allows us to do more powerful tests more easily – also, because the Central Limit Theorem provides some justification. But we choose that assumption more often because it’s the easiest way to get the most power.
