I have a population with a mean (mean_1) (which was calculated through many trials and so have a very very small uncertainty in the mean). The standard deviation of the population is 'S'.
I have a second population with mean_2 (which again has a very very small uncertainty) and a standard deviation which is again 'S'.
Say I make a single further observation and the value falls somewhere in between mean_1 and mean_2, is there a test that I can perform to say with what certainty the observation came from population 1 and what certainty it came from population 2?
Thank you.