Sean and Maria monitor the same radioactive sample. Sean counts for one minute and gets 121 events. Maria counts for six minutes and get 576 events. Each then calculates the rate in events per minute. Do their results agree satisfactorily?
Express the discrepancy as best value ± uncertainty. Base your answer on the discrepancy scaled by the uncertainty in that discrepancy. Judge the scaled discrepancy to be significant if greater than 3 SDs. Is it significant?
Note 1: The two rate values are independent random variables. Combine in quadrature.
Note 2: The uncertainties are not square roots of the rates!
Now suppose that Sean takes his measurements a great many times, so that that his rate of 121 events per minute can be taken as nearly exact. Would the scaled discrepancy now be significant (greater than 3 SDs)?
