The percentage of water removed from paper as it passes through a dryer depends on the temperature of the dryer and the speed of the paper passing through it. A laboratory experiment was conducted to investigate the relationship between dryer temperature T at three levels and exposure time E (which is related to speed). A 3 × 3 factorial experiment was conducted with temperatures at 100°, 120°, and 140°F and for exposure time T at 10, 20, and 30 seconds. Four paper specimens were prepared for each condition. The data (percentages of water removed) are shown in the table below.

a. Perform an analysis of variance for the data and construct an analysis of variance table.

b. Do the data provide sufficient evidence to indicate that temperature and time interact? Test using α = .05. What is the practical significance of this test? 

c. Fit the second-order model  

E(y) = β₀ + β₁E + β₂T + β₃(E × T) + β₄E² + β₅T²

to the data. Give the prediction equation.

d. Estimate the mean percentage of water removed when T = 120 and E = 20. Why does this value differ from the sample mean of the four observations obtained for this factor–level combination?

e. Find and interpret the 95% confidence interval for the mean percentage of water removed when T = 140 and E = 30.

Transcribed Image Text:

PAPER2 Temperature (T) 100 120 140 10 24 26 33 33 45 49 21 25 36 32 44 45 Exposure Time (E) 20 39 34 51 50 67 64 37 40 47 52 68 65 30 58 55 75 71 89 87 56 53 70 73 86 83