The following data shown were collected during an experiment to determine the change in thrust efficiency (y, in percent) as the divergence angle of a rocket nozzle (x) changes:
(a) Fit a second-order model to the data.
(b) Test for significance of regression and lack of fit using a = 0.05.
(c) Test the hypothesis that B11 = 0, using a = 0.05.
(d) Plot the residuals and comment on model adequacy.
(e) Fit a cubic model, and test for the significance of the cubic term using a = 0.05.

24.60 23.90 39.50 24.71 57.12 39.60 4.0 4.0 4.0 6.0 5.0 5.0 67.24 67.11 67.15 67.15 77.87 77.87 84.67 80.11 6.75 6.5 6.5 7.3 7.0 7.1