Variance Estimates and the F Ratio

Testing the Null Hypothesis
The two hypotheses are:
H 0 : μ 1 = μ 2 = μ 3 .
H 1 : not all μ’s are equal.
Assume that we have conducted an experiment and that
we have computed the value of F.
Suppose we could agree on a dividing line for any F
distribution, where values of F falling above the line are
considered to be unlikely (i.e., incompatible with H 0 )
and values of F falling below the line as considered to
be likely (i.e., compatible with H 0 ).