Nanowires, tiny wires just a few millionths of a centimeter thick, which spiral and have a pine tree-like appearance, have recently been created. \({ }^{2}\) The investigators' ultimate goal is to make better nanowires for high-performance integrated circuits, lasers, and biosensors. The twist, in radians per unit length, should follow a theory of mechanical deformation called Eshelby twist. The amount of twist should be linearly related to the reciprocal of cross section. The authors provided some of their data on \(y(\mathrm{rad} / \mu \mathrm{m})=\) twist and \(x\left(\mu \mathrm{m}^{-2}\right)=\) reciprocal cross section.

(a) Fit a straight line by least squares.

(b) Test, with \(\alpha=0.05\), that the slope is different from zero.

(c) Find a 98% confidence interval for the mean twist angle when \(x=148\).

(d) Does this aspect of the Eshelby twist theory seem to apply?

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