Worked Examples Population Parameters and Sample Statistics

Worked Examples: Population
Parameters vs. Sample
Statistics

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Printed: July 15, 2017

www.ck12.org Chapter 1. Worked Examples: Population Parameters vs. Sample Statistics

1CHAPTER Worked Examples:

Population Parameters vs. Sample

Statistics

Worked Examples: Population Parameters vs. Sample Statistics

Example 1

A study is to be conducted on the psychological effects of personally witnessing a jewelry store theft from a local
mall. Police records suggest that there were a total of 23 witnesses. Is this a situation that would suggest that the
entire population be included in the study, why or why not?
Solution:
The relatively small population size in this example certainly suggests that a full census be taken. A shopping mall
in likely to contain a rather broad range of demographics, and the 23 witnesses are therefore likely to have many
differences in age, sex, background, profession, etc.. Any representative sample taken would probably not be able
to accurately represent the full range of possible factors affecting the results of the study.

Example 2

A new medicine has been developed that the developer claims will stimulate hair growth in balding men. Would
you expect there to be safety tests conducted on the population of men before release?
Solution:
Read the question carefully! In statistics, “population” has a very specific meaning. It would be impossible
to conduct safety tests on every man in the world, therefore any safety tests would have to be conducted on a
representative sample, not on the population of male humans.

Example 3

The Ford Explorer is a popular sport-utility vehicle sold in the U.S. originally equipped with Firestone tires. In
May of 2000, Ford and Firestone were both accused of responsibility in hundreds of vehicle accidents caused by tire
failure. Given that all vehicles sold in the U.S. undergo extensive safety testing, how could so many bad products
have slipped through?
Solution:
There are many ways that the problem could have gone unnoticed. This is a situation where a census study of
every Explorer produced in just not feasible; much of the testing simply has to be conducted on a representative
sample. Perhaps the sample vehicles used for safety testing just happened to be ones with good tires, or perhaps the
safety tests weren’t extensive enough, or the results were incorrectly evaluated.

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Example 4

You and your team are conducting a study on the differences in the ability of students in your school to focus during

different times throughout the day. Each day your team chooses every student to walk in the

door, and you study 112 students on Monday, 78 on Tuesday, and 109 on Wednesday. If there are 299 students in
the school, is this a sample or a population?
Solution:
Even though your team collected samples equal to the population of the school, it would still be a representative
sample rather than a true census since your random selection method almost certainly resulted in the observation of
some students multiple times, and missed others entirely.

Example 5

Why would it be virtually unarguable to state that a product claiming to be “Everyone’s Favorite Soda,” has not been
properly evaluated from a statistical standpoint?
Solution:
A population study on every single person in the world is impossible.

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