_____________________________________________________________________________________________
STatistics Education Web: Online Journal of K-12 Statistics Lesson Plans 7
http://www.amstat.org/education/stew/
Contact Author for permission to use materials from this STEW lesson in a publication
test pits from Stratum II are: 96, 100, 28, 60, 89, 70, 49, 87, 29, 38. Only pit 100 contains an
artifact. Thus, the estimated total number of finds at the site is (5)(5) = 25.
For the systematic sample since there are a total of 100 test pits at the site, if we wish to obtain
20 test-pits in our sample, we need to take a 1-in-5 systematic sample. Using a SEED of 2003,
and generating an integer at random between 1 and 5, the starting test pit would be test pit #2.
After test pit 2, every 5
th
test pit is selected: 2, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67,
72, 77, 82, 87, 92, 97. Only test pit 47 contains artifacts. Thus, the estimated total number of
finds at the site would be: (5)(1) = 5.
For cluster sampling, using a SEED of 2004 and generating integers at random between 1 and
10, the selected clusters would be row 2 and row 3. So the sampled test pits are: 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30. Pits 13, 19, 20, and 25 contain
artifacts so the estimated total number of finds at the site is: (5)(4) = 20
For the simple random and stratified samples selected from Site 2 once everyone has selected
their samples and placed their results on the white board, the class results can be analyzed. Here
is some example class data for the comparison of sampling strategies for Site 2:
stratified random sampling estimated totals:
15.625, 18.750, 28.125, 15.625, 18.750, 21.875, 31.250, 9.375, 28.125, 21.875, 18.750,
18.750, 21.875, 25.000, 15.625, 25.000, 25.000, 12.500, 15.625, 25.000, 31.250, 21.875,
31.250, 25.000, 15.625, 15.625, 18.750, 25.000, 18.750
simple random sampling estimated totals:
10, 25, 5, 40, 25, 35, 20, 5, 20, 25, 35, 5, 40, 25, 20, 25, 20, 15, 10, 20, 25, 15, 30, 20, 25, 10,
10, 15, 25
For each sampling technique students calculate descriptive statistics for the class estimated total
numbers of finds. Figures 3 and 4 show descriptive statistics and comparative dotplots for the
example class results (the frequency plots made from sticky notes on the white board will
resemble the dotplots). Additionally, comparative boxplots are constructed from the class
estimated totals. Figure 5 shows comparative boxplots for the example class results.