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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 1.1.40
Chapter 1, Problem 1.1.40

Determine whether the number describes a population parameter or a sample statistic. Explain your reasoning.
Voter registration records show that 47% of all voters in a county are registered as Democrats.

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1
Identify the key terms in the problem: 'population parameter' refers to a value that describes a characteristic of an entire population, while 'sample statistic' refers to a value that describes a characteristic of a subset (sample) of the population.
Examine the context of the problem. The problem states that 47% of *all voters* in the county are registered as Democrats. The phrase 'all voters' indicates that the data pertains to the entire population of voters in the county.
Determine whether the value (47%) is describing the entire population or just a sample. Since the data is based on all voters in the county, it is describing a population characteristic.
Conclude that the number 47% is a population parameter because it represents a proportion calculated from the entire population of voters in the county, not just a sample.
Explain the reasoning: A population parameter is used when the data represents the entire group being studied, as opposed to a sample statistic, which is derived from a subset of the population.

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Key Concepts

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

Population Parameter

A population parameter is a numerical value that summarizes a characteristic of an entire population. In statistics, it is often denoted by symbols such as 'μ' for the mean or 'p' for the proportion. Population parameters are typically unknown and are estimated through sample statistics. In the given question, the 47% figure represents a characteristic of all voters in the county, making it a population parameter.
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Parameters vs. Statistics

Sample Statistic

A sample statistic is a numerical value that summarizes a characteristic of a sample drawn from a population. It is used to estimate the corresponding population parameter. Sample statistics are denoted by symbols like 'x̄' for the sample mean or 'p̂' for the sample proportion. If the 47% figure were derived from a smaller group of voters rather than the entire population, it would be considered a sample statistic.
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Voter Registration Records

Voter registration records are official documents that track the registration status of voters within a specific jurisdiction. These records provide data on various demographic characteristics, including party affiliation. In this context, the records indicate that 47% of all registered voters in the county identify as Democrats, which is crucial for understanding the political landscape and making informed decisions based on the population parameter.
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