An investigation of a die-casting process resulted in the accompanying data on x,= furnace temperature, x,= die close time, and y = temperature difference on the die surfacet. 1250 1300 1350 1250 1300 1250 1300 1350 1350 6 6 7 80 95 101 85 92 87 96 106 108 Minitab output from fitting the multiple regression model with predictorsx, and x, is given here. The regression equation is tempdiff = -200 + 0.210furntemp + 3.00clostime Fredictor Coef Stdev t-ratio Constant furntemp -199.56 11.64 -17.14 0.000 24.30 0.000 0.000 0.210000 0.000642 0.4321 clostime 3.0000 6.94 - 1.058 Analysis of£ Variance R-aq- 99.14 R-sg (adj) = 98.84 SOURCE Regression Error DF 0.000 5ר.357 1.12 2 715.50 319.31 6.72 Total 722.22 (a) Carry out the model utility test. State the appropriate hypotheses. Hi at least one , 0 O Hg: 8, - 8, 0 H at least one 8,-0 Hgi no P, = 0 Hi all P, = 0 State the appropriate test statistic to two decimal places. D19.31 State the conclusion in the problem context. O Reject H The model is useful. O Reject H The model is not useful. O Fail to reject H. The model is not useful. O Fail to reject H. The model is useful. (b) Calculate a 95% confidence interval for 8, the population regression coefficient of x. (Round your answers to three decimal places.) 1.943 (4.057 Interpret the confidence interval • Holding furnace temperature fixed, we estimate that the average change in temperature difference on the die surface will fall within this interval. O Holding both factors fixed, we estimate that the average change in temperature difference on the die surface will fall within this interval.