Type A Expmt Part 2 Exercise 4: One more thing…

The standard error on the mean is calculated as

where s is the random uncertainty on each measurement, and N is the number of times that you repeated the measurement. Does this imply that if we simply repeat the reaction time measurement many, many times (so that N is very large), that we can make the uncertainty on the average arbitrarily small i.e. can we know the average to as many decimal places as we want?