A Monte Carlo propagation of a density measurement gives a simulated relative…

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Data analysis and model fitting in the laboratory

Measurement and Method, Ch Monte Carlo and the bootstrap: uncertainty by sampling

Problem

A Monte Carlo propagation of a density measurement gives a simulated relative standard uncertainty of

2.5

per cent from

B = 100

trials. A simulated standard deviation for a bell-shaped output is known to about

1/\sqrt{2B}

of itself. ((a)) If the number of trials is increased to

B = 900

, estimate the precision (in percentage points) to which the

2.5

per cent figure is now known, and state whether the density itself has been measured any better. ((b)) Find the number of trials

B

needed so that the

2.5

per cent figure is known to

\pm 0.020

percentage points.

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