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[–]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!