The concentration of a catalyst used in producing grouted sand is thought to aff

Question

The concentration of a catalyst used in producing grouted sand is thought to affect its strength. An experiment designed to investigate the effects of three different concentrations of the catalyst utilized six test specimens of grout per concentration Analyze this data as a single factor experiment.

Concentration

35%

40%

45%

5.9

6.6

9.9

8.1

7.9

9

5.6

8.4

8.6

6.4

9.4

7.8

7.5

8.2

8.7

8.5

6.8

8.2

a) Can you conclude that at least one of the concentrations is different? Yes or No. Justify your answer.

b) Perform Tukey's test at a = .05 (you may use Minitab) to determine which pairs are different from the rest.

c) Analyze the residuals with a normal probability plot. What do you conclude / recommend?

Concentration

35%

40%

45%

5.9

6.6

9.9

8.1

7.9

9

5.6

8.4

8.6

6.4

9.4

7.8

7.5

8.2

8.7

8.5

6.8

8.2

Explanation / Answer

here we test null hypothesis H0: all concentration are same

against the alternate hypothesis H1: at least one of the concentrations is different

here level of significance alpha is not mentioned , let alpha=0.05

we used ms-excel and following anova is generated

(a) since p-value of F-test between groups is less than alpha=0.05, so we reject H0 and conclude that at least one of the concentrations is different

(b)

Tukey lsd for difference between (35% and 40%)=(7-7.88)/sqrt(1.022*(1/6 +1/6))=-1.51

Tukey lsd for difference between (35% and 45%)=(7-8.7)/sqrt(1.022*(1/6 +1/6))=-2.92

Tukey lsd for difference between (45% and 40%)=(8.7-7.88)/sqrt(1.022*(1/6 +1/6))=1.41

critical Tukey lsd(0.05,3,15)=3.67 is more than absolute value of all the 3 difference, so non of the pair of concentration is significantly different to each other

ANOVA Source of Variation SS df MS F P-value F crit Between Groups 8.674444 2 4.337222 4.244319 0.034614 3.68232 Within Groups 15.32833 15 1.021889 Total 24.00278 17

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