A Model of Classroom Research in Action: Developing Simulation Activities to Improve Students' Statistical Reasoning
Robert C. delMas and Joan Garfield
University of Minnesota
Beth L. Chance
University of the Pacific
Journal of Statistics Education v.7, n.3
(1999)
Copyright (c) 1999 by Robert C. delMas, Joan
Garfield, and Beth L. Chance, all rights reserved. This
text may be freely shared among individuals, but it may not
be republished in any medium without express written
consent from the authors and advance notification of the
editor.
Appendix A: Pretest for Sampling Distributions Activity
Name: __________________________________________
Date: _________________
On the pages that follow, you will find 5 different
problems. For each problem, a population distribution is
presented in the upper left of the page. For each
population you are asked to identify the distribution of
sample means that might result for each of two different
sample sizes.
Each problem presents five graphs labeled A through E.
The two questions for a problem are presented on the page
that is opposite the page with the graphs. To answer
each question, circle the letter that corresponds to the
graph you believe best represents the distribution of
sample means that might result for the given sample
size.
Pay careful attention to the sample sizes because they
change from question to question.
Then, read through the reasons listed below each
question and look for the ones that match, or come close to
matching, your reasons for choosing the graph you chose.
Check ALL of the listed reasons that match yours. There is
also an OTHER REASON option where you can write in a reason
that isn't listed.
- The distribution for a population of test scores is displayed below on the left. The other five graphs labeled A to E represent possible distributions of sample means for 500 random samples drawn from the population.
Population Distribution
1a. Which graph represents a distribution of sample means for samples of size 1? (circle one)
A B C D E
Check ALL of the reasons listed below that come close to explaining your choice for question 1a.
- I expect the sampling distribution to be shaped like a
NORMAL DISTRIBUTION.
- I expect the sampling distribution to be shaped like
the POPULATION.
- I expect the sampling distribution to have LESS SPREAD
than the POPULATION.
- I expect the sampling distribution to have MORE SPREAD
than the POPULATION.
- I expect the sampling distribution to have the SAME
SPREAD as the POPULATION.
- I expect the bars of the sampling distribution and the population to have the SAME HEIGHT.
- OTHER REASON:
1b. Which graph represents a distribution of sample means for samples of size 16? (circle one)
A B C D E
Check ALL of the reasons listed below that come close to explaining your choice for question 1b.
- I expect the sampling distribution to be shaped like a
NORMAL DISTRIBUTION.
- I expect the sampling distribution to have LESS SPREAD
than the POPULATION.
- I expect the sampling distribution to have MORE SPREAD
than the POPULATION.
- I expect the sampling distribution to be shaped like the POPULATION.
- I expect the sampling distribution to have the SAME SPREAD as the POPULATION.
- I expect the bars of the sampling distribution and the population to have the SAME HEIGHT.
- I expect the second sampling distribution to have MORE spread than the first.
- I expect the second sampling distribution to have LESS spread than the first.
- I expect the second sampling distribution to look MORE like the POPULATION than the first.
- I expect the second sampling distribution to look LESS like the POPULATION than the first.
- I expect the second sampling distribution to have TALLER BARS than the first.
- I expect the second sampling distribution to have LOWER BARS than the first.
- I expect both sampling distributions to have the SAME SHAPE.
- I expect both sampling distributions to have the SAME SPREAD.
- OTHER REASON:
- The distribution for an second population of test
scores is displayed below on the left. The other five
graphs labeled A to E represent possible distributions of
sample means for 500 random samples drawn from the
population.
Population Distribution
2a. Which graph represents a distribution of sample means for samples of size 4? (circle one)
A B C D E
Check ALL of the reasons listed below that come close to
explaining your choice for question 2a.
- I expect the sampling distribution to be shaped like a NORMAL DISTRIBUTION.
- I expect the sampling distribution to be shaped like the POPULATION.
- I expect the sampling distribution to have LESS SPREAD than the POPULATION.
- I expect the sampling distribution to have MORE SPREAD than the POPULATION.
- I expect the sampling distribution to have the SAME SPREAD as the POPULATION.
- I expect the bars of the sampling distribution and the population to have the SAME HEIGHT.
- OTHER REASON:
2b. Which graph represents a distribution of sample means for samples of size 16? (circle one)
A B C D E
Check ALL of the reasons listed below that come close to explaining your choice for question 2b.
- I expect the sampling distribution to be shaped like a NORMAL DISTRIBUTION.
- I expect the sampling distribution to have LESS SPREAD than the POPULATION.
- I expect the sampling distribution to have MORE SPREAD than the POPULATION.
- I expect the sampling distribution to be shaped like the POPULATION.
- I expect the sampling distribution to have the SAME SPREAD as the POPULATION.
- I expect the bars of the sampling distribution and the population to have the SAME HEIGHT.
- I expect the second sampling distribution to have MORE spread than the first.
- I expect the second sampling distribution to have LESS spread than the first.
- I expect the second sampling distribution to look MORE like the POPULATION than the first.
- I expect the second sampling distribution to look LESS like the POPULATION than the first.
- I expect the second sampling distribution to have TALLER BARS than the first.
- I expect the second sampling distribution to have LOWER BARS than the first.
- I expect both sampling distributions to have the SAME SHAPE.
- I expect both sampling distributions to have the SAME SPREAD.
- OTHER REASON:
- The distribution for a third population of test scores
is displayed below on the left. The other five graphs
labeled A to E represent possible distributions of sample
means for 500 random samples drawn from the
population.
Population Distribution
3a. Which graph represents a distribution of sample means for samples of size 1? (circle one)
A B C D E
Check ALL of the reasons listed below that come close to explaining your choice for question 3a.
- I expect the sampling distribution to be shaped like a NORMAL DISTRIBUTION.
- I expect the sampling distribution to be shaped like the POPULATION.
- I expect the sampling distribution to have LESS SPREAD than the POPULATION.
- I expect the sampling distribution to have MORE SPREAD than the POPULATION.
- I expect the sampling distribution to have the SAME SPREAD as the POPULATION.
- I expect the bars of the sampling distribution and the population to have the SAME HEIGHT.
- OTHER REASON:
3b. Which graph represents a distribution of sample means for samples of size 9? (circle one)
A B C D E
Check ALL of the reasons listed below that come close to explaining your choice for question 3b.
- I expect the sampling distribution to be shaped like a NORMAL DISTRIBUTION.
- I expect the sampling distribution to have LESS SPREAD than the POPULATION.
- I expect the sampling distribution to have MORE SPREAD than the POPULATION.
- I expect the sampling distribution to be shaped like the POPULATION.
- I expect the sampling distribution to have the SAME SPREAD as the POPULATION.
- I expect the bars of the sampling distribution and the population to have the SAME HEIGHT.
- I expect the second sampling distribution to have MORE spread than the first.
- I expect the second sampling distribution to have LESS spread than the first.
- I expect the second sampling distribution to look MORE like the POPULATION than the first.
- I expect the second sampling distribution to look LESS like the POPULATION than the first.
- I expect the second sampling distribution to have TALLER BARS than the first.
- I expect the second sampling distribution to have LOWER BARS than the first.
- I expect both sampling distributions to have the SAME SHAPE.
- I expect both sampling distributions to have the SAME SPREAD.
- OTHER REASON:
- The distribution for a fourth population of test scores
is displayed below on the left. The other five graphs
labeled A to E represent possible distributions of sample
means for 500 random samples drawn from the
population.
Population Distribution
4a. Which graph represents a distribution of sample means for samples of size 4? (circle one)
A B C D E
Check ALL of the reasons listed below that come close to
explaining your choice for question 4a.
- I expect the sampling distribution to be shaped like a NORMAL DISTRIBUTION.
- I expect the sampling distribution to be shaped like the POPULATION.
- I expect the sampling distribution to have LESS SPREAD than the POPULATION.
- I expect the sampling distribution to have MORE SPREAD than the POPULATION.
- I expect the sampling distribution to have the SAME SPREAD as the POPULATION.
- I expect the bars of the sampling distribution and the population to have the SAME HEIGHT.
- OTHER REASON:
4b. Which graph represents a distribution of sample means for samples of size 25? (circle one)
A B C D E
Check ALL of the reasons listed below that come close to
explaining your choice for question 4b.
- I expect the sampling distribution to be shaped like a NORMAL DISTRIBUTION.
- I expect the sampling distribution to have LESS SPREAD than the POPULATION.
- I expect the sampling distribution to have MORE SPREAD than the POPULATION.
- I expect the sampling distribution to be shaped like the POPULATION.
- I expect the sampling distribution to have the SAME SPREAD as the POPULATION.
- I expect the bars of the sampling distribution and the population to have the SAME HEIGHT.
- I expect the second sampling distribution to have MORE spread than the first.
- I expect the second sampling distribution to have LESS spread than the first.
- I expect the second sampling distribution to look MORE like the POPULATION than the first.
- I expect the second sampling distribution to look LESS like the POPULATION than the first.
- I expect the second sampling distribution to have TALLER BARS than the first.
- I expect the second sampling distribution to have LOWER BARS than the first.
- I expect both sampling distributions to have the SAME SHAPE.
- I expect both sampling distributions to have the SAME SPREAD.
- OTHER REASON:
- The distribution for a fifth population of test scores
is displayed below on the left. The other five graphs
labeled A to E represent possible distributions of sample
means for 500 random samples drawn from the
population.
Population Distribution
5a. Which graph represents a distribution of sample means for samples of size 1? (circle one)
A B C D E
Check ALL of the reasons listed below that come close to explaining your choice for question 5a.
- I expect the sampling distribution to be shaped like a NORMAL DISTRIBUTION.
- I expect the sampling distribution to be shaped like the POPULATION.
- I expect the sampling distribution to have LESS SPREAD than the POPULATION.
- I expect the sampling distribution to have MORE SPREAD than the POPULATION.
- I expect the sampling distribution to have the SAME SPREAD as the POPULATION.
- I expect the bars of the sampling distribution and the population to have the SAME HEIGHT.
- OTHER REASON:
5b. Which graph represents a distribution of sample
means for samples of size 25? (circle one)
A B C D E
Check ALL of the reasons listed below that come close to explaining your choice for question 5b.
- I expect the sampling distribution to be shaped like a NORMAL DISTRIBUTION.
- I expect the sampling distribution to have LESS SPREAD than the POPULATION.
- I expect the sampling distribution to have MORE SPREAD than the POPULATION.
- I expect the sampling distribution to be shaped like the POPULATION.
- I expect the sampling distribution to have the SAME SPREAD as the POPULATION.
- I expect the bars of the sampling distribution and the population to have the SAME HEIGHT.
- I expect the second sampling distribution to have MORE spread than the first.
- I expect the second sampling distribution to have LESS spread than the first.
- I expect the second sampling distribution to look MORE like the POPULATION than the first.
- I expect the second sampling distribution to look LESS like the POPULATION than the first.
- I expect the second sampling distribution to have TALLER BARS than the first.
- I expect the second sampling distribution to have LOWER BARS than the first.
- I expect both sampling distributions to have the SAME SHAPE.
- I expect both sampling distributions to have the SAME SPREAD.
- OTHER REASON:
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