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Ch. 1 - Introduction to Statistics
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 1 - Introduction to StatisticsProblem 1.1.44
Chapter 1, Problem 1.1.44

In Exercises 37–44, answer the given questions, which are related to percentages.
Percentages in Advertising In an actual ad for the Club, a device used to discourage car thefts, it was stated that “The Club reduces your odds of car theft by 400%.” What is wrong with this statement?

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1
Understand the concept of percentages: A percentage is a way of expressing a number as a fraction of 100. It is often used to compare relative sizes or to express changes in quantities.
Identify the claim in the statement: The ad claims that 'The Club reduces your odds of car theft by 400%.'
Analyze the meaning of a percentage reduction: A reduction of 100% would mean that the odds of car theft are completely eliminated. A reduction of more than 100% is mathematically nonsensical because it implies a negative probability, which is impossible.
Consider the correct interpretation: If the odds of car theft are reduced by 100%, it means there is no chance of theft. A reduction of 400% is misleading because it suggests that the odds are not only eliminated but somehow reversed, which is not possible.
Conclude the error in the statement: The statement is incorrect because it misuses the concept of percentage reduction. A more accurate claim would be to state the actual percentage reduction in risk, such as 'The Club reduces your odds of car theft by 80%' or similar, based on actual data.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Understanding Percentages

Percentages represent a fraction of 100 and are used to compare relative sizes. A percentage can indicate how much one quantity is of another, but it must be interpreted correctly. For example, saying something is reduced by a percentage implies a decrease, but exceeding 100% can lead to confusion.
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Limits of Percentage Reduction

A percentage reduction cannot exceed 100%, as this would imply a complete elimination and more. For instance, a 100% reduction means the item is gone, while a 400% reduction suggests an impossible scenario where the item is not only gone but somehow has a negative presence. This highlights the importance of logical consistency in statistical claims.
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Statistical Misrepresentation

Statistical misrepresentation occurs when data is presented in a misleading way, often to exaggerate claims. In advertising, this can lead to false impressions about a product's effectiveness. The statement about reducing theft odds by 400% exemplifies this, as it misuses statistical language to create an unrealistic perception of the product's impact.
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Related Practice
Textbook Question

In Exercises 21–28, determine which of the four levels of measurement (nominal, ordinal, interval, ratio) best describes the given data.

College Students In order to better plan for the incoming freshman class, a college dean asks each newly admitted student to identify their likely major (physics, business, math, psychology, engineering, law, etc.).

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Textbook Question

In Exercises 21–28, determine whether the study is an experiment or an observational study, and then identify a major problem with the study.

Drinking and Driving A researcher for a consortium of insurance companies plans to test for the effects of drinking on driving ability by randomly selecting 1000 drivers and then randomly assigning them to two groups: One group of 500 will drive in New York City after no alcohol consumption, and the second group will drive in New York City after consuming three shots of Jim Beam bourbon whiskey.

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Textbook Question

Discrete/Continuous Data Which of the following describe discrete data?


a. The exact heights of all NBA basketball players

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Textbook Question

In Exercises 37–44, answer the given questions, which are related to percentages.

Texting While Driving USA Today reported results from an Arity survey in which 2018 drivers were asked if they text while driving.


a. Among the respondents, 42% said that they text while driving. What is the exact value that is 42% of the number of respondents?

b. Could the result from part (a) be the actual number of respondents who said that they text while driving? Why or why not?

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Textbook Question

Exercises 5–8 refer to the study of an association between which ear is used for cell phone calls and whether the subject is left-handed or right-handed. The study is reported in “Hemispheric Dominance and Cell Phone Use,” by Seidman et al., JAMA Otolaryngology—Head & Neck Surgery, Vol. 139, No. 5. The study began with a survey e-mailed to 5000 people belonging to an otology online group, and 717 surveys were returned. (Otology relates to the ear and hearing.)

Experiment or Observational Study Is the study an experiment or an observational study? Explain.

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