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Ch. 1 - Introduction to Statistics
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 1 - Introduction to StatisticsProblem 1.1.5
Chapter 1, Problem 1.1.5

"Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
A statistic is a numerical description of a population characteristic."

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1
Understand the definition of a statistic: A statistic is a numerical description of a sample characteristic, not a population characteristic. A population characteristic is described by a parameter.
Compare the given statement to the correct definition: The statement claims that a statistic describes a population characteristic, which contradicts the definition.
Determine the truth value of the statement: Based on the definition, the statement is false.
Rewrite the statement to make it true: 'A statistic is a numerical description of a sample characteristic.'
Review the distinction between a statistic and a parameter: A parameter describes a population characteristic, while a statistic describes a sample characteristic.

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Key Concepts

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

Statistics vs. Parameter

In statistics, a 'statistic' refers to a numerical value that describes a sample, while a 'parameter' is a numerical value that describes a whole population. The statement in question incorrectly defines a statistic as a description of a population characteristic, which is actually the role of a parameter.
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Parameters vs. Statistics

Population and Sample

A population encompasses all members of a defined group, while a sample is a subset of that population selected for analysis. Understanding the distinction is crucial because statistics are often used to infer characteristics about a population based on sample data.
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Sampling Distribution of Sample Proportion

Descriptive vs. Inferential Statistics

Descriptive statistics summarize and describe the features of a dataset, while inferential statistics use sample data to make generalizations about a population. The statement's focus on a population characteristic aligns more with inferential statistics, which rely on parameters rather than statistics.
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Parameters vs. Statistics
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