Exercise 1
Visual Decision Tutor (VDT) Sampling Exercises and Simulations
Exercise 1: Construct and Compare Histograms for n = 5 and n = 50
Objective: Gain experience with random sampling and constructing histograms
(1)
(2)
(3)
(4)
(5)
Overview of Activities:
Record population values
Take a random sample
Construct and compare sample histograms and ranges to population
Combine data so that n = 50 and construct a new histogram and find new range
Discussion and Activities:
The bag of 450 beads represents a target population containing 450 population units. The
target population could be defined for contaminants in soil, water, air, on building
surfaces, etc. Each bead represents one population unit and the color of the bead
represents the true concentration of contaminant for that population unit.
(1) Record population values:
Population N
=
Sample n
=
Can we assume sampling without replacement methods apply?
In other words, is n less than 5% of N? _____(Note: 5/450 x 100% = 1.1%.)
True range, i.e., Max - Min
=
(2) Take random sample:
Without looking, randomly select five beads from bag. It is best to take two or three
beads, and then select the rest, rather than to take more than five and remove some.
(3) Construct sample histogram and find sample range:
Use black ink to color each square where a bead from the random sample should be
placed. Find sample range, i.e., sample max – sample min, and draw horizontal line the
width of your sample range in row 8. Label as, e.g., “Sample Range = 7 ppm, n = 5.”
(4) Combine data for n = 50 case:
Note that n = 50 is not less than 5% of N = 450. However, since each bag has an
identical population, we can combine the sample data from 10 people and have a
population of N = 4,500. Color in the data from 9 other people in blue ink.
How does the histogram for n = 50 compare with the population histogram? Draw a
horizontal line the width of your sample range in row 10. Label as, e.g., “Sample Range
= 13 ppm, n = 50.”
How does the range for n = 50 compare with the population range?
(5) Based on this exercise, do you believe a sample size of n = 5 is adequate to estimate
 The population range?
 The population histogram?
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Exercise 1
Visual Decision Tutor (VDT) Sampling Exercises and Simulations
Exercise 1 Simulations
(1) Observe VDT option SamplingSample Beads, Show RangeOne
Sampling Event with n = 5 for a number of trials.
Do you see much variability in the sample ranges?
(2) Observe VDT option SamplingSample Beads, Show
RangeSeventeen Sampling Events
What is the minimum range observed?
What is the maximum range observed?
How confident can you be with a sample size of 5 that you are near the correct range
for the beads population?
How well, in your opinion, do the n = 5 samples represent the population histogram?
(3) Observe VDT option SamplingSample Beads, Show RangeOne
Sampling Event with n = 50 for a number of trials.
Do you see much variability in the sample ranges?
(4) Observe VDT option SamplingSample Beads, Show Range with n = 50
for a number of trials.
What is the minimum range observed?
What is the maximum range observed?
How confident can you be with a sample size of 50 that you are near the correct range
for the beads population?
How well, in your opinion, do the n = 50 samples represent the population histogram?
(5) Observe VDT option SamplingSample Beads, Show Range with n = 450
for a number of trials.
What is the minimum range observed?
What is the maximum range observed?
How confident can you be with a sample size of 450, a census, that you are near the
correct range for the beads population?
Thought Question: In your opinion, is there much benefit, in this case, in taking n =
450 vs. n = 50 samples for estimating the range?
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