T-tests, Normality, and the Central Limit Theorem
A listener wrote in and said: "I was just listening to an old episode of Data Skeptic on the 'Student's t-distribution'.
In the episode Kyle strongly emphasized that the populations that the samples are coming from need to be normally distributed... I thought that one does not need to care what distribution governs the population (whether it is normal or not) because the sampling distribution will always be normally distributed due to Central Limit Theorem." This post is a response to this excellent question.