7 days Compressive Strength

Min=23.46 Dihydrate Hemihydrate

3%

30.4070 5.7013

24.7056 1.9004

34.2078 5.7013

4%

26.6061 3.8505

26.6061 1.9004

22.8052 3.8505

5%

15.2035 0

17.1039 0

17.1039 0

1. Define Null and Alternative Hypotheses

Ho: Dihydrate = Hemihydrate Ho: 3%=4%=5%

H1: Dihydrate ≠ Hemihydrate H1: 3%≠4%≠5%

Ho: An interaction is absent

H1: An interactin is present

2. State Alpha

Alpha=0.05

3. Calculate Degrees of Freedom

dF(a)CaSO4 =2-1=1

dF(b)concentration =3-1=2

dF(axb)=(1)(2)=2

dFerror = 18-(2)(3)=12

dFtotal=18-1=17

4. State Decision Rule

CaSO4[dF(a),dF(error)]: (1,12) CV = 4.7472

Concentration[dF(b),dF(error)]: (2,12) CV =3.8853

CaSO4xConcentration [dF(axb),dF(error)]: (2,12) CV =3.8853

These critical values bring us to our three decision rules:

[CaSO4] If F is greater than 4.7472, reject the null hypothesis.

[Concentration] If F is greater than 3.8853, reject the null hypothesis.

[Interaction] If F is greater than 3.8853, reject the null hypothesis.

5. Calculate Test Statistic

SS dF MS F

CaSO4(a) 2044.6883 1 2044.6883 350.7545

Concentration(b)

246.2037 2 123.1019 21.1174

Interaction(axb) 60.5129 2 30.2565 5.1903

Error 69.9533 12 5.8294 -

Total 2421.3582 17 - -

SSa=∑ ¿¿¿

Dihydrate Sum

=30.4070+24.7056+34.2078+26.6061+26.6061+22.8052+15.2035+17.1039+17.1039=214.7491

Hemihydrate Sum

=5.7013+1.9004+5.7013+3.8505+1.9004+3.8505=22.9044

SSa=214.74912+22.90442

3(3)−237.6535

2

18=2044.6883

SSb=∑ ¿¿¿

3% Sum=102.6234

4% Sum=85.6188

5% Sum=49.4113

SSb=102.62342+85.61882+49.41132

3(2)−237.6535

2

18=246.2037

Cell1 = 89.3204

Cell2=76.0174

Cell3= 49.4113

Cell4=13.303

Cell5 = 9.6014

Cell6=0

SSaxb = ∑ ¿¿¿

= 89.32042+76.01742+49.41132+13.3032+9.60142

(3)-214.7491

2+22.90442

3(3)-

102.62342+85.61882+49.41132

3(2)+ 237.6535

2

18

=5489.1356-5182.4208-3383.9362+3137.7326

SSaxb = 60.5129

SStotal = ∑Y 2−¿ 237.65352

18¿

= 5559.0908-237.65352

18

SS total = 2421.3582

SSerror = SStotal-SSa-SSb-SSaxb

= 2421.3582-2044.6883-246.2037-60.5129

SSerror = 69.9533

MS= ssdF

MSa = 2044.68831=2044.6883

MSb = 246.20372=123.1019

MSaxb = 60.51292=30.2565

MSerror = 69.953312=5.8294

F= MSMSerror

Fa=2044.68835.8294 =350.7545

Fb=123.10195.8294 =21.1174

Faxb=30.25655.8294 =5.1903

6. State Results

[CaSO4] If F is greater than 4.7472, reject the null hypothesis.

Our F=350.7545. Reject the null hypothesis.

[Concentration] If F is greater than 3.8853, reject the null hypothesis.

Our F = 21.1174. Reject the null hypothesis.

[Interaction] If F is greater than 3.8853, reject the null hypothesis.

Our F = 5.1903. Reject the null hypothesis.

7. Conclusion

Hemihydrate and Dihydrate have a significant difference. There was a significant difference between the three different levels of concentration. Lastly, an interaction effect between the concentration and number of hydrates on the gypsum was also present.