Recall that if Z N(0,1) and W 2(r) with Z and W independent, then by Definition 2.1.3, Z W/r has a

Recall that if Z ∼ N(0,1) and W ∼ χ 2(r) with Z and W independent, then by Definition 2.1.3, Z



W/r has a t(r) distribution. Also recall that in a one-way ANOVA with independent normal errors, a contrast has aΣ

i=1

λi ¯ yi· ∼ N aΣ

i=1

λiμi,σ 2 aΣ

i=1

λ 2 i

Ni

,

SSE σ 2 ∼ χ 2(dfE), and MSE independent of all the ¯ yi·s. Show that Σai =1 λi ¯ yi·−Σai  =1λiμi MSE Σai =1 λ 2 i /Ni ∼ t(dfE).