Engineers at the University of Massachusetts studied the viability of using semiconductor 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 current (y) and waveguide Al mole fraction (x):

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) = β_{o} + β_{1}x + β_{2}x^{2}, to the data using the method of least squares.

d. Conduct a formal test of the researchers’ theory. Use α = .10.