Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2010 / Paper 1 / Section A / 6

For background-subtracted radiative temperature uncertainty, assume the two quoted precisions are independent standard uncertainties, and treat the radiative proportionality factor as known. Write $P_B=B$ and $P_T=10B$. Then $P_S=9B$, while both absolute input uncertainties equal $0.5B$. ConsequentlyThus the temperature precision is about $1.96\%$, or $2\%$. Subtraction amplifies fractional uncertainty even though $P_T$ itself is precise.

Independence is a measurement assumption, not a consequence of the two percentages. For correlation coefficient $r_c$, the result is ${\sigma }_T/T=\sqrt{2(1-r_c)}/72$. If the percentages are strict error bounds combined pessimistically, the corresponding bound is $2.78\%$. Unknown calibration correlations cannot be inferred from the source.