December 3rd. Use a significance level (a) of 0.05 if not specified. 60 total points. Part 2 - Give detailed solution supplemented by important outputs from Minitab. 9. (15 pts) The manufacturer of a certain brand of freeze-dried coffee hopes to shorten the processing time without jeopardizing the integrity of the product. He wants to use 3 temperatures for the drying chamber and 3 drying times. The current drying time is 3 hours at a temperature of -15C. The flavor response is an average of scores of 4 professional judges. The score is on a scale from 1 to 10 with 10 being the best. A factorial design is employed here with two replicates at each condition. The data and some statistics are in Table 1. a. What is the appropriate statistical model for this experimental design? Conduct an analysis of variance on the experiment results. How is the flavor of freeze-dried coffee effected by the temperature? by the time? and by their interaction? b. Assuming that the standard deviation is 0.15, is the number of replicates (2) adequate to detect a maximum difference of 0.25 in scores among any pair of temperature or time means with a power of more than 0.9 to reject the equal means hypothesis? Explain. c. What settings would you recommend for the two factors if high score of flavor is desired? (Construct necessary interaction plots and/or main effect plots to support your answer) Table 1 Temperature Time -20 C -15 C -10C 1 hr 9.60, 9.63 9.55, 9.50 9.40, 9.43 2 hr 9.82, 9.93 9.81, 9.78 9.50, 9.52 3 hr 9.78, 9.81 9.80, 9.75 9.55, 9.58 December 3rd. Use a significance level (a) of 0.05 if not specified. 60 total points. Part 2 - Give detailed solution supplemented by important outputs from Minitab. 9. (15 pts) The manufacturer of a certain brand of freeze-dried coffee hopes to shorten the processing time without jeopardizing the integrity of the product. He wants to use 3 temperatures for the drying chamber and 3 drying times. The current drying time is 3 hours at a temperature of -15C. The flavor response is an average of scores of 4 professional judges. The score is on a scale from 1 to 10 with 10 being the best. A factorial design is employed here with two replicates at each condition. The data and some statistics are in Table 1. a. What is the appropriate statistical model for this experimental design? Conduct an analysis of variance on the experiment results. How is the flavor of freeze-dried coffee effected by the temperature? by the time? and by their interaction? b. Assuming that the standard deviation is 0.15, is the number of replicates (2) adequate to detect a maximum difference of 0.25 in scores among any pair of temperature or time means with a power of more than 0.9 to reject the equal means hypothesis? Explain. c. What settings would you recommend for the two factors if high score of flavor is desired? (Construct necessary interaction plots and/or main effect plots to support your answer) Table 1 Temperature Time -20 C -15 C -10C 1 hr 9.60, 9.63 9.55, 9.50 9.40, 9.43 2 hr 9.82, 9.93 9.81, 9.78 9.50, 9.52 3 hr 9.78, 9.81 9.80, 9.75 9.55, 9.58
