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# Analysis of variance (ANOVA)

The results shown below are mean productivity measurements (average number of assemblies completed per hour) for a random sample of workers at each of three plants. Research question: Are the mean hourly productivity levels the same for workers in these three plants?

Productivity

Hourly Productivity of Assemblers in Plants
Plant Finished Units Produced Per Hour
A (9 workers) 3.6 5.1 2.8 4.6 4.7 4.1 3.4 2.9 4.5
B (6 workers) 2.7 3.1 5.0 1.9 2.2 3.2
C (10 workers) 6.8 2.5 5.4 6.7 4.6 3.9 5.4 4.9 7.1 8.4

#### Solution Preview

The results shown below are mean productivity measurements (average number of assemblies completed per hour) for a random sample of workers at each of three plants. Research question: Are the mean hourly productivity levels the same for workers in these three plants?

Hourly Productivity of Assemblers in Plants
Plant Finished Units Produced Per Hour

A (9 workers) 3.6 5.1 2.8 4.6 4.7 4.1 3.4 2.9 4.5
B (6 workers) 2.7 3.1 5 1.9 2.2 3.2
C (10 workers) 6.8 2.5 5.4 6.7 4.6 3.9 5.4 4.9 7.1 8.4

A B C
3.6 2.7 6.8
5.1 3.1 2.5
2.8 5 5.4
4.6 1.9 6.7
4.7 2.2 4.6
4.1 3.2 3.9
3.4 5.4
2.9 4.9
4.5 7.1
8.4

Mean= 3.9667 3.0167 5.57
Variance= 0.685 1.1977 2.9779
Sample size= 9 6 10

nT= 25 = 9 + 6+10
k=no of samples= 3

1) Hypothesis
Null Hypothesis: H0: M 1=M 2=M 3 (The means are the ...

#### Solution Summary

Tests the hypothesis that the mean hourly productivity levels the same for workers in the three plants using Analysis of variance (ANOVA).

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