Exercise 2.2 Let y11,y12, . . . ,y1r be N(1, 2) and y21, y22, . . .

Exercise 2.2 Let y11,y12, . . . ,y1r be N(μ1,σ 2) and y21, y22, . . . ,y2s be N(μ2,σ 2)

with all yi js independent. Write this as a linear model. For the rest of the problem use the results of Chapter 2. Find estimates of μ1, μ2, μ1 −μ2, and σ 2. Using Appendix E and Exercise 2.1, form an α = .01 test for H0 : μ1 = μ2. Similarly, form 95% confidence intervals for μ1−μ2 and μ1. What is the test for H0 : μ1 = μ2+Δ , whereΔ is some known fixed quantity? How do these results compare with the usual analysis for two independent samples?