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The null hypothesis in ANOVA one-way classification, the study of the variances due to k different sources, is:
1. H0 ∶ σ1 = σ2 = ⋯ = σk
2. H∶ At least for one pair μi = μj; i, j = 1, 2…k, i ≠ j
3. H∶ At least for one pair σi = σj; i, j = 1, 2…k, i ≠ j
4. H∶ μ1 = μ2 = ⋯ = μk

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Correct Answer - Option 4 : H∶ μ1 = μ2 = ⋯ = μk

Explanation:

The hypotheses of interest in an ANOVA are as follows:

  • H0: μ1 = μ2 = μ3 ... = μk
  • H1: Means are not all equal.

 

Where k = the number of independent comparison groups.

In this example, the hypotheses are:

  • H0: μ1 = μ2 = μ3 = μ4
  • H1: The means are not all equal.

 

The null hypothesis in ANOVA is always that there is no difference in means. The research or alternative hypothesis is always that the means are not all equal and is usually written in words rather than in mathematical symbols.

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