Problem 4 Problem 5.31 in [Montgomery 2013], use only the data and answer the following questions. Use R and assume that larger values of density and surface area are preferred. a. Do any of the factors, or their interactions, affect powder density? Test assumptions. If any of the factors are determined to affect the response, which levels stand out? b. Do any of the factors, or their interactions, affect surface area? Test assumptions. if any of the factors are determined to affect the response, which stand out? c. Take the results of both response variables and draw conclusions about the factors and levels. d. Suppose that the specifications require that surface area must be between 0.3 and 0.6 cng and that density must be less than 14 g/cm3. Find a set of operating conditions that will result in a product that meets these requirements. 5.31. An article in Quality Progress (May 2011, pp. 42-48) describes the use of factorial experiments to improve a silver powder production process. This product is used in conduct tive pastes to manufacture a wide variety of products ranging from silicon wafers to elastic membrane switches. Powder density (g/em ) and surface area (cm /g) are the two critical characteristics of this product. The experiments involved three factors-reaction temperature, ammonium percent, and stir- ring rate. Each of these factors had two levels and the design was replicated twice. The design is shown below. Ammonium Stir Rate Temperature Surface (RPM) (C) Density Area 100 14.68 0.40 100 15.18 0.43 30 100 15.12 0.42 30 100 8 17.48 0.41 2 150 8 7.54 0.69 150 8 6.66 0.67 30 150 12.46 052 30 150 12.62 0.36 2 100 40 10.95 0.58 2 100 40 17.68 0.43 30 100 40 12.65 0.57 30 100 40 15.96 054 2 150 40 8.03 0.68 2 150 40 8.84 0.75 30 150 40 14.96 0.41 30 150 40 14.96 0.41(a) Analyze the density response. Are any interactions sig- nificant? Draw appropriate conclusions about the effects of the significant factors on the response.Problem 5 Problem 5.28 in [Montgomery 2013]. only part a, by R. 5.13. A maratt'aettner of laundry matinee.- is investigating the perfonnamze of a newly formulated stain remoter. The new formulation is coronal-ed to the original formulation: with respect to its ability to mmove a standard tomato-like stain in a test article of moon cloth using a litetwin] experiment. The other factors in the experiment are the number of times the test article is washed {1 or 2) and whether or not a detergent btmster is used. The rte-spouse variable is the stain shade after washing {D is the darkest. 0 is the lightest). The data are shown in the following table. Number of Number of Washing Washing l 2 Formulation Booster Booster Yes No Yes No New 6. S 6. S 3. 2 4. l Original It]. 9 II, II It). 9 9. 10 to) Conduct an analysis of variance. Using a: = 0.05. what conclusions can you that