A researcher studying four different populations proposes the following:
H_0 ∶ μ_1=μ_2=μ_3=μ_4
H_1 ∶ not all μ_i are equal (i=1,2,3,4)
He takes samples from each of the populations, obtaining the following data:
Group 1 Group 2 Group 3 Group 4
Sample mean 110 105 91 102
Sample size 8 9 5 6
The within-group variation of the data (SSW) is equal to 108.
Using the Tukey-Kramer procedure, calculate the critical range for making a comparison of groups 1 and 4.
Using the data and your answer to part (a), explain whether or not the null hypothesis should be rejected.