Confidence Limits on Simulation Averages 2.
Imagine repeating this experiment many (infinity) times, each time taking a sample of size n.
If we say “67% of all the sample means <m> lie within [some value] of the true mean.”…
…then [some value] serves as a confidence limit
According to the Central Limit Theorem, the distribution of observations of the sample mean <m> will follow a gaussian, with
Our confidence limit is then
We can only estimate this using the sample variance