3. The coating experiment, described in Excercise 7 of Chapter 7, was to study the effect of different spray parameters on thermal spray coating properties. In the experiment, the authors attempted

to produce high-quality alumina (Al2O3) coatings by controlling the fuel ratio (factor A at 1:2.8 and 1:2.0), carrier gas flow rate (factor B at 1.33 and 3.21 L s-¹), frequency of detonations (factor C at 2 and 4 Hz), and spray distance (factor D at 180 and 220 mm). To quantify the quality of the coating, the researchers measured multiple response variables. In this example we will examine the porosity (vol. %). The data are shown in the table below and can be downloaded from http: //deanvossdraguljic.ietsandbox.net/DeanVossDraguljic/SAS-data.html. A B с D Yijkl A B C D 2 2 2 2 5.95 2 2 2 1 2 2 1 2 1 4.57 4.03 2.17 1 2 2 2 1 2 2 2 2 1 1 1 2 1 2 1 1 1 1 1 2 1 1 1 1 2 2 1 2 1 2 1 2 Yijkl 12.28 9.57 6.73 6.07 8.49 4.92 6.95 5.31 1 2 2 3.43 2 1 2 1 1.02 2 1 1 2 4.25 2 1 1 1 2.13 1 1 1 1 (a). [3pts]. Run a model with ALL main-effects and two-way interaction effects. Write down the SAS code copy the ANOVA table from SAS. and (b).[2pts] The 95% confidence interval for the difference between the two main effects of B is ( (c).[2pts] Do you believe there are significant interaction effects between B and C? Answer yes or no. (d).[3pts] Generate an interaction plot for the B*C interaction. State how the plot supports your answer in c. [Hint: use 1smeans B*C to get the least squares estimates, then plot it using any software of your choice.] (e).[3pts] The 90% confidence upper limit for the error variance o² is Show your work.