AP Statistics: 200% of Nothing Take-Home Test
Fr. Chris Thiel, OFMCap
2 October 1997
Pick 5 of the following to answer. Answers should be typed
and grammatically accurate. Illustrations may be used when relevant.
Answers should be 1/2 to 2 pages in length per question (1-1.25"
margins, doubled spaced, 12pt font)
- "Number Numbness" (coined by Douglass Hofstadter)
refers to the inability for people to comprehend very large or
very small numbers. An example of this is the casual way that
people perceive different nation's gross national product (GNP).
Find a way to effectively communicate the vast difference between
a million, a billion and a trillion.
- Describe the ambiguity in the claim: "In recent side-by-side
blind taste tests, nationwide, more people preferred Pepsi
over Coca-Cola"
- Find an actual chart that has been published in a newspaper,
pamphlet, or magazine that demonstrates "Chart Abuse."
Comment on what has been done to distort the information it displays.
- In a democracy, polls can be a valuable tool for finding public
opinion. Care needs to be taken to find an accurate assessment.
Name three factors that could distort the results of a survey
and what could be done to minimize their impact.
- What is "compounding"? If you were a salesperson
wanting to convince someone that they should finance $10,000 over
36 months at 11% rather than pay the $10,000 outright, how could
you deceive the unsuspecting customer (see page 13 for ideas)?
Where is the flaw in your deception?
- What is "percentage pumping"? Consider the case
of a new refrigerator that uses less energy, saving money. The
old model uses $150 a year in electricity and the new model consumes
only $90 a year in electricity. Explain how to compute the savings
correctly (in terms of percentage), and then show how an unscrupulous
sales representative can exaggerate this savings by using the
"percentage pumping" formula.
- What is meant by "inummeracy"? Is it a problem
in the United States today? Cite examples of innumeracy and why
is might have a serious impact on society.
- Would you trust in a new miracle drug because of a report
that 50 people were cured by it in clinical trials? Why or why
not?
- You think of someone during the course of the day, and later
they call you on the telephone or you receive a correspondence
from them "out of the blue." Is this a shocking coincidence?
Discuss the likelihood of this phenomenon when compared to winning
the lottery. (Be sure to use the ideas of "number numbness"
and "expected outcome")
- Your Uncle Fritz says "I'd swear on a stack of bibles
that the full moon makes people drive like raving maniacs"
(or perhaps "lunatics" would be a better word choice!).
To back up his opinion, he rattles off a list of incidents where
he had a number of "near misses" around the time of
a full moon. Describe how data "filtering" could effect
your uncle's perceptions.
E-mail instructor: cct@ktb.net
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