A group measuring the resistivity of a length of copper wire (Chapter 5's method)…
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Problem
A group measuring the resistivity of a length of copper wire (Chapter 5's method) takes batches of ten resistance readings and, after each batch, recomputes the running mean resistivity ρˉ and its standard uncertainty u(ρˉ). The manufacturer's data sheet quotes ρsheet=1.68×10−8Ωm. The group's rule is: stop as soon as ρˉ agrees with ρsheet to within u(ρˉ), or after 10 batches, whichever comes first. Suppose the wire's true resistivity (unknown to the group) is ρ=1.75×10−8Ωm, some way from the data-sheet figure.
((a)) Is this a fixed stopping rule in the sense required for an unbiased result?
((b)) Predict, with a reason, whether the published mean is on average closer to 1.68×10−8Ωm or to 1.75×10−8Ωm, compared with a measurement that used a number of batches fixed in advance.