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 cm2/g 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 201 1, 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 (gfem ) 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 2 100 14.68 0.40 100 00 15.18 0.43 100 15.12 0.42 100 17.48 0.41 150 7.54 0.69 150 6.66 0.67 150 12.46 052 150 12.62 0.36 88NNSENNSS NNSSN 100 40 10.95 0.58 100 40 17.68 0.43 100 40 12.65 0.57 100 15.96 0.54 150 40 8.03 0.68 150 8.84 0.75 150 14.96 0.41 150 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