The diameter of a wire is measured with a micrometer screw gauge

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

The diameter of a wire is measured with a micrometer screw gauge. The gauge's calibration certificate states a systematic uncertainty of

\pm 0.003\,\mathrm{mm}

in any diameter it reports; this bound comes from the calibration and is not reduced by repeating the reading. Twelve repeated readings of the same wire, taken with care to avoid the ratchet slipping, give a sample standard deviation

s = 0.015\,\mathrm{mm}

. ((a)) Find the number of readings

N

at which the standard error of the mean first falls to the size of the

0.003\,\mathrm{mm}

calibration bound. ((b)) Find the number of readings

N

at which the standard error of the mean falls to about a third of that bound, the working rule for how many readings are worth taking. ((c)) Only twelve readings have been taken so far. State how many further readings, beyond the twelve, are needed to reach the target of part (b).

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