The percentage of hardwood concentration in raw pulp (4%, 8%, 10%, 12%), the vat pressure (500, 750 psi), and the cooking time of the pulp (2, 4 hours) are being investigated for their effects on the mean tensile strength (kN/m) of paper. Four levels of hardwood concentration, two levels of pressure, and two cooking times are selected. The data from the experiment (in the order collected) are shown in the following table.
Hardwood (%) Pressure (psi) Cook Time (hours) Strength
12 500 2 6.91
12 500 4 8.67
12 500 2 6.52
4 750 2 6.87
12 750 4 6.99
12 500 4 8.01
12 750 2 7.97
4 500 2 5.82
10 500 4 7.96
8 750 4 7.31
8 750 2 7.05
10 500 4 7.84
8 500 2 6.06
4 750 4 6.95
10 750 2 7.40
8 750 2 6.94
4 500 4 7.20
8 500 2 6.23
10 500 2 5.99
4 750 4 6.87
8 750 4 6.80
10 750 2 7.31
12 750 2 7.81
10 750 4 7.41
4 500 2 6.04
4 750 2 6.71
8 500 4 7.82
8 500 4 7.45
4 500 4 7.30
12 750 4 7.21
10 750 4 7.45
10 500 2 6.53
(a) Perform an ANOVA to determine if hardwood concentration, pressure, and/or cooking time affect the mean tensile strength of paper. Use α=0.05.
(b) Prepare appropriate residual plots for your ANOVA analysis and comment on the model’s adequacy.
(c) Which levels of hardwood concentration, pressure, and cooking time should you use to maximize mean tensile strength.
(d) Find an appropriate regression model for this data.
(e) Prepare appropriate residual plots for your regression analysis and comment on the model’s adequacy.
(f) Using the regression equation you found in part c, predict the tensile strength for a hardwood concentration of 9%, a pressure of 650 psi, and a cooking time of 3 hours.
(g) Find a 95% prediction interval for the tensile strength for a hardwood concentration of 9%, a pressure of 650 psi, and a cooking time of 3 hours.