The values of the response variable of a population are: u1 = 2, u2 = 3, u3 = 4, u4 = 5, u5 = 7, u6 = 9.

(a) Determine the mean and the variance 2 of the population.

(b) Compute the mean and variance of y for a simple random sample of size 4 of this population.

(c) Suppose the population is divided into two strata: stratum 1 contains u1 = 2, u2 = 3, u3 = 4, while stratum 2 contains u4 = 5, u5 = 7, u6 = 9. Determine the average and the empirical variance in each of the two strata.

(d) List all samples of size 4 that can be selected by choosing simple random samples of 2 units in each of the strata. For each global sample of size 4, give the probability that it is selected.

e) For each sample obtained in (d), calculate the stratified mean ySTR of the sample.

f) Verify that E(ySTR) = and

V(USTR) N - 1 1 1