An electronic metronome ticks at an interval of exactly
PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement
Measurement and Method, Ch Repeated readings: scatter, the mean and the standard error
Problem
An electronic metronome ticks at an interval of exactly 2.000s, accurate to 1 part in 104, which is treated as exact for this problem. The metronome is timed with a hand-held stopwatch, pressing the button on a tick to start and on a later tick to stop. Two kinds of timing are done, twenty times each, always by the same operator: timing a single tick-to-tick interval (nominal 2.000s): mean reading xˉ1=2.07s, sample standard deviation s1=0.14s, N=20; timing five consecutive tick-to-tick intervals (nominal 10.000s): mean reading xˉ5=10.09s, sample standard deviation s5=0.15s, N=20. The metronome's own timing is essentially exact, so any scatter or offset in the readings comes from the operator's button presses.
((a)) Using how s1 and s5 compare, estimate the order of magnitude of the scatter contributed by the operator's reaction time to a single timing.
((b)) The mean readings exceed the true values by about 0.07s (single interval) and 0.09s (five intervals). Decide whether this excess behaves as a random or a systematic effect, giving the reasoning in terms of how its size compares across the two chain lengths and what happens to it on averaging.
((c)) If 180 more single-interval timings were taken (so N=200 in total), by roughly what factor would the standard error of the mean single-interval reading shrink, and would this touch the 0.07s excess?