Robert A. Millikan (1865-1953) produced the first accurate measurements on the charge \(e\) of an electron. He devised a method to observe a single drop of water or oil under the influence of both electric and gravitational fields. Usually, a droplet carried multiple electrons, and direct calculations based on voltage, time of fall, etc., provided an estimate of the total charge.

(a) Find the equation of the least squares line for Millikan's data.

(b) Find a 95% confidence interval for the slope \(\beta\), the charge \(e\) on a single electron.

(c) Test the null hypothesis \(\alpha=0\) against the alternative hypothesis \(\alpha eq 0\).

(d) Examine the residuals.

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x (No. of e's) 34526 Observations (10 x charge) 1.392 1.392 1.398 1.768 1.768 1.910 2.471 2.471 2.256 1.368 1.368 1.368 1.345 1.768 1.746 1.746 1.886 2.256 2.471 1.768 1.768 1.768 0.944 0.992 2.981 2.688