Question

Please find the test statistic for EACH of the above three hypothesis

Using the data from we want to use the Bonferonni method to test the following hyptheses at the 3% significance level:

Group 1	Group 2	Group 3
4.2	4.5	1.2
5.3	2.2	−0.3
3.4	2.3	0.6
		2.6

H₀ : μ₁ = μ₂       H₁ : μ₁ ≠ μ₂
H₀ : μ₁ = μ₃       H₁ : μ₁ ≠ μ₃
H₀ : μ₂ = μ₃       H₁ : μ₂ ≠ μ₃

(a)	Find the value of the test statistic for each of the above three hypotheses (in the above order).

(b)	Which pairs of means are significantly different (using the Bonferonni method at the 3% significance level)?

Answer 1

applying ANOVA on above data:

Source	SS	df	MS	F	P value
Treatment	19.0725	2	9.5363	6.9193	0.021969
Error	9.6475	7	1.3782
Total	28.7200	9

critical value of t with 0.01 level and N-k=7 degree of freedom=				tN-k=	3.499
Bonferroni crtiical value for group i and j =(tN-k)*(sp*√(1/ni+1/nj)   =						3.35

a) test statistic for each of the above three hypotheses =(xi-xj)/se)= 1.356 , 3.653 ,2.203

b)

Signiifcant difference are between pairs 1 and 3