Assume that 12 = 22 = 2. Calculate the pooled estimator of 2 for each of the

Question:

Assume that σ12 = σ22 = σ2. Calculate the pooled estimator of σ2 for each of the following cases:
a. s12 = 200, s22 = 180, n1 = n2 = 25
b. s12 = 25, s22 = 40, n1 = 20, n2 = 10
c. s12 = .20, s22 = .30, n1 = 8, n2 = 12
d. s12 = 2,500, s22 = 1,800, n1 = 16, n2 = 17
e. Note that the pooled estimate is a weighted average of the sample variances. To which of the variances does the pooled estimate fall nearer in each of cases a–d?