ANOVA Analysis
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Given the following number of hours between breakdowns for 4 machines, are the machines significantly different? If so, how are they different? Which machine is the best? Which machine is the worst? You are to perform a thorough and complete analysis of the data. Use alpha = .05 for all tests.
Machine 1 Machine 2 Machine 3 Machine 4
6.4 8.7 11.1 9.9
7.8 7.4 10.3 12.8
5.3 9.4 9.7 12.1
7.4 10.1 10.3 10.8
8.4 9.2 9.2 11.3
7.3 9.8 8.8 11.5
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Solution Summary
The solution provides step-by-step method of performing an Analysis of Variance or ANOVA Hypothesis Test. All the steps of hypothesis testing (formulation of null and alternate hypotheses, selection of significance level, choosing the appropriate test-statistic, decision rule, calculation of test-statistic and conclusion) have been explained in details. A separate Excel sheet showing the ANOVA analysis has also been included.
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Solution:
State the Null and Alternate Hypothesis
The null hypothesis in ANOVA states that the mean number of hours between breakdowns for all the 4 machines is the same.
The alternate hypothesis in ANOVA states that the mean number of hours between breakdowns for all the 4 machines is not the same.
H_0:μ_1=μ_2=μ_3=μ_4
H_1:μ_1≠μ_2≠μ_3≠μ_4 ...
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