Consider an experiment designed to compare four treatment means1, 2, 3, and 4using sample sizes of size n1, n2, n3, and n4 and sample variances

Consider an experiment designed to compare four treatment means—μ1, μ2, μ3, and μ4—using sample sizes of size n1, n2, n3, and n4 and sample variances s21, s22, s23, and s24.
a. Suppose the sample sizes are the same: n1 = n2 = n3 = n4. Show that s2W is the average of the four sample variances: s2W = (s21, + s22, + s23, + s24)/4.
b. Does this hold if the sample sizes are not equal? If not, why not just use the average?