I've just started a beginner's statistics course, and they've presented us with the variance of the sample mean as:
$$ \operatorname{Var} \left[ \bar X_m \right] = \frac{N-n}{N-1} \frac {\sigma^2} n$$
where, as I understand it, $\bar X_m$ is the mean of $m$ random variables, each of size $n$, from a population of $N.$
But, in looking this up, I've also seen this formula: $\operatorname{Var} [\bar X_m] = \frac {\sigma^2} n$
I take it both are right under different circumstances, and I've tried looking it up, but can't seem to find when to use one and when the other?
Any insight would be greatly appreciated, thanks so much.