51. *This exercise motivates the formula for the between estimate of the variance in one-way ANOVA. Suppose the sample sizes all equal n and the population means all equal . The sampling distribution of each Y, then has mean and vanance o/n. The sample mean of the values, when the sample sizes are equal. is simply F.

a) Treatmg F, 2.,, as g observations having the sample mean Y, explain why ( )/(g 1) estimates the variance o/n of the distribution of the P-values.

b) Using (a), explain why n(-)/(-1) estimates o. For the unequal sample size case, replacing n by n, yields the between estimate.