A metrology group wants to detect a systematic voltage offset of against a null of…

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Probability, statistics and stochastic methods · Probability, statistics and stochastic methods

Error, Chance and the Machine, Ch Tests, intervals and Bayesian inference

Problem

A metrology group wants to detect a systematic voltage offset of

\mu_1 = 1.0\ \mathrm{mV}

against a null of zero offset. Each measurement is an independent Gaussian reading with known standard deviation

\sigma = 3.0\ \mathrm{mV}

and mean equal to the true offset. They will use the one-sided Neyman-Pearson test of

H_0:\mu=0

against

H_1:\mu=\mu_1

at significance

\alpha = 0.05

(one-sided normal quantile

z_{0.05}=1.645

), and they require power

1-\beta = 0.90

against

\mu_1

(one-sided normal quantile

z_{0.10}=1.282

). How many independent measurements

n

are needed, rounded up to a whole number?

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