Chapter 11.1, Problem 15E

The power curves of Figures 10.5 and 10.6 can be used to obtain β = P(type II error) for the F test in two-factor ANOVA. For fixed values of α₁, α₂,…, α_I, the quantity ${\varphi }^2=(J/I){\displaystyle \sum {\alpha }_i^2/{\sigma }^2}$ is computed. Then the figure corresponding to v₁ = I − 1 is entered on the horizontal axis at the value f, the power is read on the vertical axis from the curve labeled v₂ = (I – 1)(J – 1), and β = 1 − power.

a. For the corrosion experiment described in Exercise 2,find β when α₁ = 4, α₂ = 0, α₃ = α₄ = 22, and σ = 4. Repeat for α₁ = 6, α₂ = 0, α₃ = α₄ = −3, and σ = 4.

b. By symmetry, what is β for the test of H_0B versus H_aB in Example 11.1 when β₁ = .3, β₂ = β₃ = β₄ = −.1,and σ = .3?