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One-way Analysis of Variance (ANOVA)

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A company wishes to test 4 different types of tires, A, B, C, D. The lifetimes of the tires, as determined from their treads, are given (in thousands of miles) in the Table (*see attached), where each type has been tried on 6 similar automobiles assigned at random to tires. Test at the (a) 0.05, (b) 0.01 levels whether there is a difference in tires.

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In this problem, a one-way analysis of variance (ANOVA) experiment is analyzed. The problem is solved step by step by showing all calculations for doing the analysis by hand and explains each step in detail.

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Solution:

This is an example of a One-way Analysis of Variance. It is a technique for testing the null hypothesis that all four means are the same vs. the alternative that at least one of the means differs from the others.

Independent samples of size n = 6 were randomly selected from the distribution of tire lifetimes for the 4 types of tires. It is necessary for this test to assume all 4 distributions have a normal distribution and that the variances of all 4 distributions are approximately the same.

Before beginning the procedure, one must calculate the sample means for each of the tire lifetime samples.

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