Cesium atoms cooled by laser light could be used to build inexpensive atomic clocks. In a study reported in IEEE Transactions on Instrumentation and Measurement (2001, Vol. 50, pp. 1224€“1228), the number of atoms cooled by lasers of various powers were counted. The data are in Table E11-19.

(a) Graph the data and fit a regression line to predict the number of atoms from laser power. Comment on the adequacy of a linear model.

(b) Is there a significant regression at α = 0.05? What is the P-value?

(c) Estimate the correlation coefficient.

(d) Test the hypothesis that ρ = 0 against the alternative ρ ‰  0 with α = 0.05. What is the P-value?

(e) Compute a 95% confidence interval for the slope coefficient.

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Number of Power (mW) Atoms (×10E9) 11 0.02 12 18 0.08 0.13 21 22 0.15 24 0.18 28 0.31 32 0.4 37 0.49 39 0.57 0.64 41 0.71 46 0.79 48 0.82 50 51 0.83