The data presented in the following table give the tensile strength in psi (y) of paper as a function of the percentage of hardwood content (x).

Hardwood Tensile Hardwood Tensile Content Strength Content Strength 1.0 26.8 7.0 52.1 1.5 29.5 8.0 56.1 2.0 36.6 9.0 63.1 3.0 37.8 10.0 62.0 4.0 38.2 11.0 62.5 4.5 41.5 12.0 58.0 5.0 44.8 13.0 52.9 5.5 44.7 14.0 38.2 6.0 48.5 15.0 32.9 6.5 50.1 16.0 21.9

a. Fit polynomial models of degrees 1, 2, and so on, to predict tensile strength from hardwood content. For each one, use the F test to compare it with the model of degree one less. Stop when the P-value of the F test is greater than 0.05. What is the degree of the polynomial model chosen by this method?

b. Using the model from part (a), estimate the hardwood concentration that produces the highest tensile strength.