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)

  1. "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.

  2. Describe the ambiguity in the claim: "In recent side-by-side blind taste tests, nationwide, more people preferred Pepsi™ over Coca-Cola™"

  3. 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.

  4. 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.

  5. 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?

  6. 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.

  7. 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.

  8. 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?

  9. 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")

  10. 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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