Homework SourseAn experimentis conductedtoinvestigatetheeffects of four met
An experimentis conductedtoinvestigatetheeffects of four metal oxides on severalcementproperties. The four factors are all run at two levels and one response of interest is the mean bulk density(g/cm3). The four factors and their levels are
Factor
Low Level (-1)
High Level (+1)
A: %Fe2O3
0
30
B: %ZnO
0
15
C: %PbO
0
2.5
D: %Cr2O3
0
2.5
Typical results from this type of experiment aregiven in thefollowingtable:
Run
A
B
C
D
Density
1
-1
-1
-1
1
2.001
2
1
-1
-1
-1
2.062
3
-1
1
-1
-1
2.019
4
1
1
-1
1
2.059
5
-1
-1
1
-1
1.990
6
1
-1
1
1
2.076
7
-1
1
1
1
2.038
8
1
1
1
-1
2.118
Test ifthe main factoreffectsaresignificantor not. Test alsothesignificanceof 2-way interactioneffects. (Use a significancelevel of =0.10)
| Factor | Low Level (-1) | High Level (+1) |
| A: %Fe2O3 | 0 | 30 |
| B: %ZnO | 0 | 15 |
| C: %PbO | 0 | 2.5 |
| D: %Cr2O3 | 0 | 2.5 |
Solution
Analysis of Variance for C1 (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 0.0111375 0.00568076 0.00142019 * *
A 1 0.0089111 0.00000560 0.00000560 * *
B 1 0.0013781 0.00004978 0.00004978 * *
C 1 0.0008201 0.00061678 0.00061678 * *
D 1 0.0000281 0.00071881 0.00071881 * *
2-Way Interactions 3 0.0013224 0.00132237 0.00044079 * *
A*B 1 0.0000911 0.00009113 0.00009113 * *
A*C 1 0.0005281 0.00052813 0.00052813 * *
A*D 1 0.0007031 0.00070312 0.00070312 * *
Residual Error 0 * * *
Total 7 0.0124599
Estimated Coefficients for C1 using data in uncoded units
Term Coef
Constant 2.04537
A 0.0333750
B 0.0131250
C 0.0101250
D -0.00187500
A*B -0.00337500
A*C 0.00812500
A*D -0.00937500
here the the experiment done in one replicate hence the MSE will not defined. only sum of square can be obtained. The sum of square are given above.
