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Ch. 1 - Introduction to Statistics
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Triola 14th EditionCh. 1 - Introduction to Statistics문제 1.1.41
1장, 문제 1.1.41

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?

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1
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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주요 개념

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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.
추천 영상:
가이드 코스
06:21
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.
추천 영상:
가이드 코스
06:21
Step 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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06:29
How to Create Frequency Distributions
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교과서 질문

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

Sleep Study When designing the study of a new treatment for insomnia in adults, researchers were criticized because their test subjects consisted of 75 college students. They then expanded the study so that 750 college students were given the treatment.

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교과서 질문

In Exercises 13–20, determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance.


Bias in Jury Selection In the case of Casteneda v. Partida, it was found that during a period of 11 years in Hidalgo County, Texas, 870 people were selected for grand jury duty, and 39% of them were Americans of Mexican ancestry. Among the people eligible for grand jury duty, 79.1% were Americans of Mexican ancestry.

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교과서 질문

In Exercises 9–20, identify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster.

Cormorant Density Cormorant bird population densities were studied by using the “line transect method” with aircraft observers flying along the shoreline of Lake Huron and collecting sample data at intervals of every 20 km (based on data from Journal of Great Lakes Research).

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교과서 질문

In Exercises 29–36, identify what is wrong.

Healthy Water In a USA Today online poll, 951 Internet users chose to respond, and 57% of them said that they prefer drinking bottled water instead of tap water.

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교과서 질문

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

Criminology In a criminology study, the lengths of prison sentences are obtained for randomly selected subjects convicted of auto theft.

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교과서 질문

In Exercises 21–24, refer to the sample of body temperatures (degrees Fahrenheit) in the table below. (The body temperatures are from Data Set 5 in Appendix B.)

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Conclusion If we analyze the listed body temperatures with suitable methods of statistics, we conclude that when the differences are found between the 8 AM body temperatures and the 12 AM body temperatures, there is a 64% chance that the differences can be explained by random results obtained from populations that have the same 8 AM and 12 AM body temperatures. What should we conclude about the statistical significance of those differences?

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