Question

The following is the sample information. Test the hypothesis at the 5% level of significance that the treatment means are equal. Present your solution by the p value method

Treatment 1	Treatment 2		Treatment 3
9	13		10
7	20		9
11	14		15
9	13		14
12			15
10
Anova: Single Factor
SUMMARY
Groups	Count	Sum		Average		Variance
Treatment 1	6	58		9.66666667		3.066667
Treatment 2	4	60		15		11.33333
Treatment 3	5	63		12.6		8.3
ANOVA
Source of Variation	SS	df		MS		F	P-value
Between Groups	70.4	2		35.2		5.117932	0.024704
Within Groups	82.53333333	12		6.87777778
Total	152.9333333	14

Answer 1

H₀: ?₁ = ?₂ = ?₃ all the means are the same

H₁: Two or more means are different from the others

Here, we are trying to test whether the means of the three groups are the same or are different. This is a case of one way ANOVA.

Now as we are given here the level of significance of 0.05, and the p-value here is 0.025 < 0.05, therefore the test is significant and we can reject the null hypothesis here and conclude that there are at least two of the means which are not the same.

Therefore the test is significant and all the means are not the same here.