Question

A civil engineer conducted a study to compare the compressive strength of concrete obtained using four different aggregates. The results of his experiment are given in the dataset file. a) Does there seem to be differences between the average strengths of concrete with different aggregates? Use ?=0.05. b) Identify the differences and specify which aggregate would you recommend if maximum compressive strength is desired. c) Check the required assumption for the test used in part (a).

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Answer 1

One-way ANOVA: C2 versus C1

Method

Null hypothesis         All means are equal
Alternative hypothesis At least one mean is different
Significance level      ? = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
C1           4 1, 2, 3, 4

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
C1       3    4898 1632.7    12.81    0.000
Error   12    1529   127.4
Total   15    6427

Model Summary

      S    R-sq R-sq(adj) R-sq(pred)
11.2888 76.21%     70.26%      57.70%

Means

C1 N    Mean StDev       95% CI
1   4 297.25 11.95 (284.95, 309.55)
2   4 315.75 13.38 (303.45, 328.05)
3   4 293.50 10.91 (281.20, 305.80)
4   4 266.75   8.30 (254.45, 279.05)

Pooled StDev = 11.2888

p-value = 0.000 < 0.05

hence we reject the null

there is significant evidence that means differ

level 2 has highest confidece interval (303.45, 328.05)

hence we select aggregate 2