• Author / Uploaded
• Raymond Baldelovar

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13-7. The compressive strength of concrete is being studied, and four different mixing techniques are being investigated. The following data have been collected. (a) Test the hypothesis that mixing techniques affect the strength of the concrete. Use α = 0.05. (b) Find the P-value for the F-statistic computed in part (a). (c) Analyze the residuals from this experiment.

Solution: a) Null and alternative hypotheses: H0 : µ1 = µ2 = µ3 = µ4. versus Ha: Not all population means are equal. Set significant level α = 0.05. 

P-value approach: (Obtained by the ANOVA table provided by R)

Table 1: Analysis of Variance Table Response: Compressive Strength Source of Sum of Degrees of Variation Squares Freedom Mixing 489740 3 Technique Residuals 153908 12 Total 643648 15

Mean Square

F0

Pr(>F)

163247

12.728

0.0004887

12826

Since P-value= 4.887 × 10−4 < 0.05 = α, we do reject the null hypothesis. It means that techniques affect the mean strength of the concrete.

b) from the table above: P-value= 4.887 × 10−4 ≅ 0

c) At significant level α = 0.05, the data do provide sufficient evidence to conclude that the residuals are acceptable.

ANOVA Graphs: