Homework 02: Comparing sampling plans

Estimating parameters under different sampling plans

Sometimes we may need to choose between two sampling plans by comparing measures such as variance, bias and accuracy. Here we are interested in estimating $\mu$, the population mean.

For purposes of studying sampling distributions, assume that all population values are known: $y_1=98,y_2=109,y_3=154,y_4=133,y_5=190,y_6=175$. Out of the $N=6$ total possible values to sample from, we will choose $n=3$.

Plan 1: The following eight possible samples may be chosen with equal probability: {1,3,5}, {1,3,6}, {1,4,5}, {1,4,6}, {2,3,5}, {2,3,6}, {2,4,5}, {2,4,6}

Plan 2: The following three samples may be chosen: {1,4,6}, {2,3,6}, {1,3,5} with respective probabilities $\delta$ = (.25, .5, .25).

Answer the following questions:

a) What is the value of $\mu$?

b) For each sampling plan, find: i)$E[\overline{y}]$, ii) $V[\overline{y}]$, iii)$\text{Bias}(\overline{y})$, iv) $MSE(\overline{y})$, where $\overline{y}$ is the mean of sample values.

c) Which sampling plan do you think is better, and why?