TITLE: What does it mean when a statistician says I’m 90% confident that the mean of the population is between 1 and 9?
QUESTION [8 upvotes]: Does that mean if I draw samples from the population that 90% of the time I'll get a number between 1 and 9?
Added: assume normal distribution for the population.

REPLY [2 votes]: When you draw a sample, you don't get a number; you get a list of numbers.  Or more precisely, a sample is a list of numbers.
No, it is not true that 90% of those numbers in the list are between $1$ and $9$, nor is it true that $90\%$ of the time, when you take a sample, anything in particular will be between $1$ and $9$.
A confidence interval depends on the list of numbers that you get in a sample.  Say you take a sample of $20$ numbers, and the resulting confidence interval for the population mean is the interval from $1$ to $9$.  Typically a much smaller proportion than $90\%$ of the numbers in the sample are between $1$ and $9$, and not infrequently, none of them are.
Now say you take another random sample of $20$ numbers from the same population, and the resulting confidence interval is from $2$ to $8.5$.  And then you take another random sample of $20$ from the same population, and the confidence interval you get is from $1.5$ to $11$.  And so on.  Then $90\%$ of the time, the interval you get will include the population mean.  That is what it means.