Hmm. Well first off, I am pretty sure you should make sure you are using the [t-distribution], not the normal distribution. Using that, I would generate a confidence interval for each individual bot. I am nearly certain that there is a way to generate a confidence interval from the mean of several other intervals. I can't remember off the top of my head but I vaguely recall it being something like the square root of the sum of the squares of the standard errors (not standard deviations since the sample size is presumably fairly small). I'll tell you if I can find it.