The value of y(i) for each of the N=8 units in the whole population. The index set for the population is:

u = {1,2,3,4,5,6,7,8}

The values of y(i) are

i ; 1 2 3 4 5 6 7 8
y(i); 1 2 4 4 7 7 7 8

For the population noted above, find the sampling distribution of bar(y) for

a. an SRS of size 3 (without replacement)

b. an SRSWR of size 3 (with replacement).

For each, draw the histogram of the sampling distribution of bar(y). Which sampling distribution has the smaller variance, and why?