5. GenAg, Inc., a genetics engineering laboratory specializing in the production of better seed varieties for commercial agriculture, is analyzing the yield response to fertilizer application for a new variety of barley that it has developed. GenAg has planted 40 acres of the new barley variety and applied a different fixed level of fertilizer to each one-acre plot. In all other respects, the cultivation of the crop was identical. The GenAg scientists maintain that the relationship between observed levels of yield, in bushels per acre, and the level of fertilizer applied, in pounds per acre, will be a quadratic relationship as Yi = {30 + {3di + {32fl + Vi, where fi is the level of fertilizer applied to the ith one-acre plot, the (3's are fixed parameters, and the V;'s are iid random variables with some continuous probability density function for which E Vi = 0 and var(V;) = a2 •