Question

# Please find the test statistic for EACH of the above three hypothesis Using the data from...

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 : μ1μ2
H0 : μ1 = μ3       H1 : μ1μ3
H0 : μ2 = μ3       H1 : μ2μ3

 (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)?

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

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