The data in the following table resulted from an experiment

The data in the following table resulted from an experiment that utilized a completely randomized design. Test the null hypothesis H_0 that Mu_1 = Mu_2 = Mu_3, where Mu_i represents the true mean for treatment i, against the alternative hypothesis H_a, that at least two of the means differ. Use alpha = 0.01.

Solution

Using technology, we get these results for one-way anova:

As P = 0.064 > 0.01, we fail to Reject Ho.

Thus, there is no significant evidence that at least two of the means differ. [CONCLUSION]

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	3	6	2	1
Column 2	3	3	1	0
Column 3	3	9	3	1
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	6	2	3	4.5	0.064	10.92477
Within Groups	4	6	0.666667
Total	10	8