This is my problem: I need to sample from a random variable that I assume to have a gaussian distribution. I want to estimate the mean and the std of the variable by doing as little sample as possible.
Is there any kind of statistical significance indicator that that can tell me, essentially, when to stop if I want to have a certain margin of safety on the mean value that I have sampled?
To synthetize, i am trying to sample incrementally and trying to stop as early as possibile given that each sample is costly, and i need some formal assurance on the probability of the real mean being somewhere near the sample mean.