Goals
Notes
Goals:
I Use Venn Diagrams to visualize sets.
I Define populations and samples.
I Identify parameters and statistics.
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What is a Venn Diagram?
Notes
A Venn diagram shows the logical relationship between sets.
A set is a collection of objects. In Venn diagrams, a set is drawn as a
shape. The logical relationships are that the sets may overlap or not
touch or be inside each other.
Example: Call ”living creatures that fly” set A, and call ”living
creatures that walk on two legs” set B.
Draw the Venn diagram for sets A and B.
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What is a Venn Diagram?
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Notes
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Why use Venn diagrams?
Notes
For statistics, Venn diagrams visualize the relationship between
populations and samples.
A population is the set of all outcomes, responses, measurements, or
counts that are of interest. A sample is a subset of the population.
Tips:
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Sample data should represent a population’s characteristics.
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Samples that aren’t randomly collected are of no value.
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An Example
Notes
Example: In a recent Gallop poll, about 600 Utahns were asked if
they donated money to a charity or volunteered time to an
organization. 48% said yes to both. (www.gallop.com)
Venn diagram:
Responses of all Utahns
Responses of Utahns in Gallop poll
The data set consist of about 288 yes’s and 312 no’s.
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More Examples
Notes
(1) Indentify the population and sample.
(2) What does the data set consist of?
Example 1 A February 2014 survey of 1000 US adults found 49%
that think buying a home is the best investment a family can make.
(http://www.rasmussenreports.com/
Example 2 A recent National Health and Nutrition Examination
Survey reports 17% of youth in the US are obese from 9120
participants.(jama.jamanetwork.com/article.aspx?articleid=1832542)
Example 3 Voluteers who had 8 hours of sleep were three times
more likely to answer questions correctly on a math test than were
sleep deprived participants. (www.cbsnews.com/news/sleep-on-it/)
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Two Numerical Descriptions of Sets
Notes
A parameter is a numerical description of a population characteristic.
A statistic is a numerical description of a sample characteristic.
Note:
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A sample statistic can vary from sample to sample.
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A population parameter remains constant for a population.
Example: A company employs 150 people. We can numerically
describe the average annual salary for all employees. Is this a
population parameter or sample statistic?
The same company has a board of directors. Draw this relationship in
a Venn diagram.
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Two Numerical Descriptions of Sets
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More Examples
Notes
Decide whether the numerical value describes a population parameter
or a sample stastic.
Example 1 A survey of 21,914 alumni report that the average
starting salary of a physical therapy / exercise science degree is
$54,259. (studentsreview.com)
Example 2 The 2182 students who accepted offers to Northwestern
University in 2009 have an average SAT score of 1444.
(www.northwestern.edu)
Example 3 There is currently 58% of the governors of the 50 states
in the United States that are Repulicans. (www.nga.org)
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Two Braches of Statistics
Notes
Descriptive statistics is the branch of statistics involving the:
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organization,
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summarization (Example: means, deviations),
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and display of data (Examples: tables or graphs).
Inferential statistics is the branch of statistics that involes using a
sample to draw conclusions about a population.
Example A large sample of men, aged 48, was studied for 18 years.
For unmarried men, approximately 70% were alive at age 65. For
married men, 90% were alive at age 65.
Statements in blue are descriptive. A possible conclusion such as,
”being married is associated with a longer life for men,” is inference.
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Drawing Conclusions
Notes
Drawing conclusions is a subjected and open-ended process. What
inferences could be drawn for the following studies? One possible
conclusion answers, ”Is there or is there not an association for in the
study?”
Example 1 In a sample of Wall Street analysts, the percentage who
incorrectly forecasted high-technology earnings in a recent year was
44%.
Example 2 A survey of 546 U.S. women found that more than 56%
are the primary investors in their households.
Example 3 A survey of 791 people on vacation found that they
planned on spending at least $2000 for their next vacation.
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Assignment
Notes
For May 16 - 2014
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§1.1 # 45, 46, 47, 49 (Due: May 19)
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Read §1.2 by May 19.
Suggested Exercises: §1.1 #1, 3, 4, 15, 23, 27, 37, 41.
You should be able to:
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Distinguish between a population and a sample.
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Distinguish between a parameter and a statistic.
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Distinguish between descriptive statistics and inferential statistics.
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