Question

Let N  6 and n  3. For purpose of studying sampling distributions, assume
that all population values are known. Specically, y1  98, y2  102, y3  154,
y4  133, y5  190, and y6  175. We are interested in yU, the population
mean. Two sampling plan are proposed.

Plan 1. Eight possible samples may be chosen.

Sample
Number Sample,S P(S)

1 (1,3,5) 1/8
2 (1,3,6) 1/8
3 (1,4,5) 1/8
4 (1,4,6) 1/8
5 (2,3,5) 1/8
6 (2,3,6) 1/8
7 (2,4,5) 1/8
8 (2,4,6) 1/8

Plan 2. Three possible samples may be chosen.

Sample
Number Sample, S P(S)

1 (1,4,6) 1/8
2 (2,3,6) 1/8
3 (1,3,5) 1/8

a What is the value of yU?
b Let y be the mean of the sample values. For each sampling plan nd
E(y), Var(y), bias(y), and MSE(y).
c Which sampling plan do you think is better? Why?