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Question 01) An engineer is designing a new battery for use in a device that will be subject to some extreme variations in temperature. The engineer decides to test all three plate materials at three temperature levels (Le, 15, 70, IZSF) as these temperatures are consistent with the product end-use environment. Four batteries are tested at each combination of plate material and temperature, and all 36 tests are run in random order. The experiment and the given resulting observed battery life data are given in the following table: mm: ___'_me_____ 13:! 15 70 125 I 130' ' 153' 34 40 20 10 - 74 130 so is 82 53 2 150 188 136 :22 25 70 I59 [26 106 I 15 58 45 3 BB no 174 120 96 [04 use too 150 I39 32 so a) What is your recommended model for this study? Fit your suggested model and include all the necessary assumptions. b) Plot the interaction plot for this example. c) Fit 3 model to connect the battery life to the main effects of temperature and plate materials in addition to the interaction effect. Report your model. d) Use Anova to study the main effects of temperature and plate materials in addition to the interaction effect. Report your Anova model. e) Write the hypotheses for the main and interaction effects that you can read from Anova. t) Interpret your results. Are the main and interaction effects at signicant level a = 0.05? g) Utilizing the 0-0 plot and residual plots check whether you model is adequate. Question 02) An experiment was conducted to determine whether either ring temperature or furnace position affects the baked density of a carbon anode. The data are as follows: Tern erature C Position 300 _z;- 350 570 -E- 565 1 565 510 583 -IE_ 590 528 526 2 547 538 521 m- 532 a) Plot the interaction plot for this example. b) Write the hypotheses for the main and interaction effects. c) Use Anova to study the main effects of temperature and position in addition to the interaction effect. Report your Anova model. d) Interpret your results. Are the main and interaction effects at signicant level a: = 0.05? e) Utilizing the 0-0 plot and residual plots check whether you model is adequate