Consider a population of 8 units (y1, ..., y8) = (15, 34, 35, 36, 11, 17, 36, 15). Suppose

you take a simple random sample of size 3 with replacement.

a. List all possible values of the sample total T.

b. Find the sampling distribution of the sample total T.

c. Let zi = 1 if unit i is selected into the sample and zi = 0 otherwise.

Calculate the correlation of zi, zj .

d. Recalculate the sampling distribution of T when sampling without replacement.

e. Recalculate the correlation of zi, zj when sampling without replacement.

f. Calculate mean and variance of the sample total T for both sampling with

and without replacement distributions.