Please show all work An experiment was conducted to determine whether either fir

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Please show all work

An experiment was conducted to determine whether either firing temperature or furnace position each at two levels, affects the baked density of carbon anode. Three replicates of this design are run. Below a partially completed estimate table and ANOVA table for the experiment. a. Calculate all the missing values in the ANOVA table b. Write the appropriate hypothesis and use this table to test for the significance of the effects. Use alpha = 0.05. c. Find all the missing values in the estimate table. Indicate which effects are significant. Use alpha = 0.05 d. Write the least squares fitted model using only the significant effects. e. Use the model to predict the response when x_1 = -1, x_2 = 1. f. Use the means table below to construct the interaction plot. Does the plot agree with your results on (c), why? g. Compute an approximate 95% CI for each effect. Compare your results with those in (c).

Explanation / Answer

a) ANOVA Table

b)

H0: There is no significance difference among the levels of Position
H1: There is significance difference among the levels of Position
P-value of Position = 0.00067496 < alpha 0.05, so we reject H0
Thus, we conclude that there is significance difference among the levels of Position

H0: There is no significance difference among the levels of Temperature
H1: There is significance difference among the levels of Temperature
P-value of Temperature = 1.6645E-11 < alpha 0.05, so we reject H0
Thus, we conclude that there is significance difference among the levels of Temperature

H0: There is no significance difference among the levels of Position*Temperature
H1: There is significance difference among the levels of Position*Temperature
P-value of Positin*Temperature = 0.4201 > alpha 0.05, so we accept H0
Thus, we conclude that there is no significance difference among interaction of Temperature * Position

c)

H0: There is no significance difference among the levels of Position
H1: There is significance difference among the levels of Position
P-value of Position = 0 < alpha 0.05, so we reject H0
Thus, we conclude that there is significance difference among the levels of Position

H0: There is no significance difference among the levels of Temperature
H1: There is significance difference among the levels of Temperature
P-value of Temperature = 0 < alpha 0.05, so we reject H0
Thus, we conclude that there is significance difference among the levels of Temperature

H0: There is no significance difference among the levels of Position*Temperature
H1: There is significance difference among the levels of Position*Temperature
P-value of Positin*Temperature = 0.724278188 > alpha 0.05, so we accept H0
Thus, we conclude that there is no significance difference among interaction of Temperature * Position

d)

The regression equation is
Density = 793.17 -24.17Position +240.83 Temperature

e)

The regression equation is
Density = 793.17 -24.17(-1) +240.83(1)
= 1058.17

Source df Sum of square mean Square F P-value Pos 1 7008 7008 28.76552 0.00067496 Temp 1 696008 696008 2856.883 1.6645E-11 Pos*Temp 1 176 176 0.722422 0.4200586 Error 8 1949 243.625 Total 11 705141

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