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?