Interpretation of Hypothesis Testing Decisions for ANOVA

H0: Means are alike
H1: Not all means are alike (means differ)
 

Part 1 of interpretation:
           Reject H0 --- We have strong evidence of H1.
Cannot reject H0 --- We do not have strong evidence of H1.

Part 2 of interpretation:
To substitute words for H1:

There is the variable that you consider and there are categories (treatments, populations) that you compare.  You want to know if the mean of the variable is different for different categories.

H1 says the mean of __variable__ is different according to __categories___.

Think of the variable involved and the categories being compared.
In the text problem, the variable was machine errors, and the categories were machine speeds.  So H1 says that the mean machine errors differ according to machine speed.

So if we reject H0 in the text problem, we say we have strong evidence that the mean machine error will differ for different machine speeds.