Some of the most common **misconceptions about confidence intervals** are:
* “There is a 95% chance that the true population mean falls within the confidence interval.” *(FALSE)*
* “The mean will fall within the confidence interval 95% of the time.” *(FALSE)*
While I do know the true definition of confidence intervals, I wonder why the above are not true?
In: Mathematics
Aleatory vs epistemic probability goes kinda beyond ELI5 stuff, so let’s put that in a box and lock the box up and put a hungry tiger on top to guard it.
The first statement is false because the probability that this confidence interval includes the true mean isn’t 95%, it’s either exactly zero or exactly one — you just don’t know which.
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