1. Intro to Stats and Collecting Data
Intro to Stats
2:49 minutesProblem 1.1.41
Textbook Question
In Exercises 37–44, answer the given questions, which are related to percentages.
Percentages in Advertising An ad for Big Skinny wallets included the statement that one of their wallets “reduces your filled wallet size by 50%–200%.” What is wrong with this statement?
Verified step by step guidance1
Identify the meaning of percentage reduction: A percentage reduction refers to the decrease in size relative to the original size. A 100% reduction would mean the size is reduced to zero.
Analyze the statement 'reduces your filled wallet size by 50%–200%': A 50% reduction means the wallet size is reduced to half of its original size. However, a 200% reduction implies the size is reduced by twice its original size, which is not possible.
Understand the logical error: A reduction greater than 100% is illogical because it suggests the size becomes negative, which is not feasible in physical terms.
Consider the implications of the statement: The claim of a 200% reduction is misleading and mathematically incorrect, as it suggests an impossible scenario.
Conclude the analysis: The statement should be revised to accurately reflect a realistic percentage reduction, such as 'up to 50%' or another feasible percentage, to avoid misleading consumers.
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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 or changes. In the context of the ad, understanding how percentages work is crucial to evaluate the claim of reducing wallet size. A reduction of more than 100% is mathematically impossible, as it implies that the wallet would not only be empty but also somehow gain size in the negative direction.
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Step 1: Write Hypotheses
Interpreting Claims in Advertising
Advertising often uses exaggerated or misleading claims to attract consumers. It's important to critically analyze such statements to determine their validity. In this case, the claim of reducing wallet size by 50%–200% raises questions about its truthfulness and the practical implications of such a reduction, which can mislead potential buyers.
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06:21Step 1: Write Hypotheses
Mathematical Limits
Mathematical limits refer to the boundaries of numerical values in a given context. In this scenario, a reduction of 200% suggests that the wallet would shrink beyond its original size, which is not feasible. Understanding these limits helps in assessing the realism of claims made in advertisements and ensures that consumers are not misled by impossible figures.
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