Homework 2
ES 714, Spring 2006
Instructor: Thaddeus Tarpey
At a large industrial site, many drums of industrial solvent have been buried in the past. A
survey is to be conducted in order to try and attempt to determine how many drums have
been buried at the site. The drums are shown in the figure on the next page (represented
by the small dots). In order to conduct the survey, the site has been partitioned into a
grid of squares (marked by the dashed lines in the figure). Additionally, the site has been
partitioned into strata (denoted by the thick lines). It is thought that the distribution of
the drums differs among the stratum.
For your homework assignment, estimate the total number of drums at the site and the
standard error of the total estimate using three different sampling designs described below.
In each case, obtain a sample of size n= 25.
1. Obtain a simple random sample. Briefly describe how you obtained your sample.
List the sampling units obtained and the corresponding number of drums at each of
the selected sites. Give the estimated total and its standard error.
2. Obtain a stratified random sample. Allocate the n= 25 observations according
to a proportional allocation. Be sure to indicate which sampling units are obtained
and list the corresponding data. Compute the estimated total and its standard error
using the stratified random sampling formulas.
3. Obtain a systematic sample. Describe how you obtained the systematic sample,
the sampling units you obtained and the corresponding data, the estimated total and
its estimated standard error. Estimate the total and its standard error using the same
formulas that are used for simple random sampling.
Note: You may run into difficulties when obtaining your samples. Indicate how you dealt
with the problems.
