The inspiration for this thread is the following question: "Without further calculation, say whether the observations are consistent with the set of values [1.215; 1.216; 1.209; 1.212] independently reported for c." I had previously found that c = 1.150259067 = 1.15 (3sf) and from error analysis that STDEV(c) = 0.0631654689 = 0.06 (1sf). Now, I am wondering what, fundamentally, we would do to find out whether data is in agreement with a value we have estimated by some other means. I am tempted to (as a general way of handling such queries) take the mean of the data set (here it would be 1.213) and compare to c +/- 1*STDEV(c) (here it would be 1.213424536 which is larger than 1.213, hence we would say "agreement" on this basis) but something does not ring right about this approach. The data set has two values outside 1 standard dev of the predicted mean. Not only that, but the error of the data set is 3.5*10-3 and the mean value found is nowhere near this close to the c value found earlier. Just from inspection, we can see how odd these measurements would be if our value of c were correct. I suspect this would barely pass a 2% right-tail hypothesis test. So how do we judge whether the calculated value is consistent with the newly measured data?