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An experimentis conductedtoinvestigatetheeffects of four metal oxides on several

ID: 3395606 • Letter: A

Question

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

Explanation / Answer

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.