A digital balance's calibration certificate gives a bound of on any single weighing
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
A digital balance's calibration certificate gives a bound of ±0.015g on any single weighing, an effect that repeated weighings cannot remove. Repeated weighings of one sample give, from N=9 readings, a sample standard deviation s=0.045g.
((a)) Calculate the standard error of the mean of the 9 readings.
((b)) Someone argues: "Doubling the number of readings halves the standard error, so with N=18 readings the standard error will fall to 0.0075g, well below the certificate's bound." Calculate the actual standard error at N=18 and say what is wrong with the reasoning.
((c)) Using the rule that readings are worth taking until the standard error falls to about a third of the largest effect repetition cannot remove, estimate how many readings would be worth taking here, and say whether N=18 is enough.