A microbalance is used to weigh a sample repeatedly

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Measurement and Method, Ch Type A, Type B and the uncertainty budget

Problem

A microbalance is used to weigh a sample repeatedly, and the sample standard deviation of the readings is found to be

s = 0.045\,\mathrm{mg}

regardless of how many readings are taken. For each of the following numbers of readings

N

, find the standard uncertainty of the mean and the

95\,\%

expanded uncertainty using t factors for

\nu = N-1

degrees of freedom (from the printed table:

t_{3,95}=3.18

t_{5,95}=2.57

t_{10,95}=2.23

). ((a))

N=4

((b))

N=6

((c))

N=11

For each case also state by what percentage the

95\,\%

interval is wider than

k=2

times the standard uncertainty, and comment on the trend as

N

increases.

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