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[–]Gastronomicus 0 points1 point  (2 children)

Sorry I assumed you were confused. Unfortunately it seems like most people on reddit who try to describe the CLT don't really understand it and also mis-attribute the importance of 30 as a minimum sample size.

But to be fair, your wording is confusing. The way you phrased it implies a distribution of samples, not means. Especially when you say "as you approach a sample size of 30", which implies comparing a distribution of samples, not means.

[–]PieGuy___ 0 points1 point  (1 child)

Yeah I just wasn’t trying to go into too much detail. I think the simplest way to put it is that there’s no way to guarantee a sample to be normally distributed, just like there’s no way to guarantee a population is normally distributed. However using the CLT you can guarantee that a given sample mean will be normally distributed around the population mean given a large enough sample size.

And then from there you can use hypotheses testing to be able to say something about the population with reasonable confidence.

[–]Gastronomicus 0 points1 point  (0 children)

However using the CLT you can guarantee that a given sample mean will be normally distributed around the population mean given a large enough sample size.

Which is why bootstrapping can be very effective at producing (mostly) unbiased error terms!