Write out a 22 design, displaying the A, B, and AB columns for the four runs.

(a) If X1,X2,X3, and X4 are the four observations for the respective runs in standard order, write out the three linear forms, [A], [B], and [AB], that measure the two main effects and the interaction. These linear forms should include the divisor 22 = 4.

(b) Show that

(c) Under the null hypothesis that all the means are equal and with the usual assumptions (normality, mutual independence, and common variance), what can you say about the distributions of the expressions in (b) after each is divided by σ2?

Linear Programing ch 19 Oct. wed 12 Linear Programming Model The goal maximization or minimization Decision variables Amounts either inputs or outputs Constraints Limitations restrict available alternatives Parameters Numerical values Linear Programming Assumptions Linearity Impact decision variables is linear in constraints & objective function Divisibility Non-integer...