Chapter 12.A.2, Problem 1Q

Suppose an experimenter has taken three independent measurements on each of five treatment levels and intends to use the analysis of variance to test

$H_0:{\text{μ}}_1={\text{μ}}_2={\text{μ}}_3={\text{μ}}_4={\text{μ}}_5\left(=0\right)$

versus

$H_1:$ not all the ${\text{μ}}_j’\text{s}$ are equal

Two of the possible alternatives in ${\text{H}}_1$ are

$H_1^{*}:{\text{μ}}_1=-1,{\text{μ}}_2=2,{\text{μ}}_3=0,{\text{μ}}_4=1,{\text{μ}}_5=-2$

And

$H_1^{**}:{\text{μ}}_1=-3,{\text{μ}}_2=2,{\text{μ}}_3=1,{\text{μ}}_4=0,{\text{μ}}_5=0$

Against which alternative will the F test have the greater power? Explain.