Solar lighting with lasers. Engineers at the University of Massachusetts studied the viability of using semiconduc- tor lasers for solar lighting in spaceborne applications (Journal of Applied Physics, Sept. 1993). A series of n = 8 experiments with quantum-well lasers yielded the following observations on solar pumping threshold cun (y) and waveguide Al mole fraction (x): SOLAR2 Threshold Current y, A/cm 2 Waveguide Al Mole Fraction x 273 .15 175 .20 146 .25 166 .30 162 .35 165 .40 245 .50 314 .60 a. The researchers theorize that the relationship between threshold current (y) and waveguide Al composition (x) will be represented by a U-shaded curve. Hypothesize a model that corresponds to this theory. b. Plot the data points in a scattergram. Comment on the researchers' theory. c. Fit the quadratic model, E(y) = B + Bx + Bx, to the data using the method of least squares. d. Conduct a formal test of the researchers' theory. Use = .10.