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May 28, 2021 at 11:32 comment added Uzu Lim Thanks for the answer, I was roughly aware of the subtlety arising from confidence interval interpretation, but that's certainly an answer worth reading. My question is roughly about how to use the convergence rate of CLT to account for the difference of the (rescaled) true distribution of the sample mean from the standard normal distribution.
May 27, 2021 at 11:48 comment added Frans Rodenburg Not sure I understand (2), but as for (1): A confidence interval in general does not give you the probability that $\mu \in [a,b]$. See the excellent answer here.
May 27, 2021 at 8:06 history asked Uzu Lim CC BY-SA 4.0