A gauge block is measured to have length (a standard uncertainty from repeated readings)

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

Measurement and Method, Ch Do two results agree? Comparison, consistency and outliers

Problem

A gauge block is measured to have length x=5.020±0.010 mmx = 5.020 \pm 0.010\,\mathrm{mm} (a standard uncertainty from repeated readings). Its accepted (calibrated) length is x0=5.000±0.008 mmx_0 = 5.000 \pm 0.008\,\mathrm{mm}. Someone argues: "the accepted value is exact, so only my own uncertainty counts, and z=5.020−5.0000.010=2.0z = \frac{5.020-5.000}{0.010} = 2.0 shows the measurement disagrees with the calibration." ((a)) Calculate the correct consistency ratio, including the accepted value's uncertainty. ((b)) State whether the measured and accepted lengths are consistent. ((c)) Explain what this comparison does and does not demonstrate about the measuring instrument.

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