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All courses Algebra II · S-IC.1 47 of 55
Understand statistics as inference about population parameters from random samples.

Separate population, frame, sample, unit, and size

Problem
A study selects \(500\) voters from the city voter-registration list to estimate the preference of all registered city voters. Identify the target population, sampling frame, sample, and observational unit.
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Hint

Identify whom/what the conclusion is intended to describe, then identify who/what was actually accessible and measured.

Population is the target group; frame is the accessible selection source; sample is the observed subset; unit is one measured entity.

Solution walkthrough

01

Identify the inference target

\[\text{target}~\text{population}=\text{all}~\text{registered}~\text{city}~\text{voters}\]

This is the full group whose preference the study intends to estimate.

02

Identify the selection source

\[\text{sampling}~\text{frame}=\text{city}~\text{voter}-\text{registration}~\text{list}\]

The frame is the operational list from which the sample is actually drawn.

03

Identify the observed subset

\[\text{sample}=500~\text{selected}~\text{voters}\]

These are the units chosen from the frame to provide data.

04

Identify one unit and conclude

\[\text{Target}:~\text{all}~\text{registered}~\text{city}~\text{voters}.~\text{Frame}:~\text{the}~\text{voter}~\text{registration}~\text{list}.~\text{Sample}:~\text{the}~500~\text{selected}~\text{voters}.~\text{Unit}:~\text{one}~\text{registered}~\text{voter}.\]

The observational unit is the individual entity on which preference is measured.

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Another way

  1. Ask four questions in order: whom to learn about, where names come from, who was selected, and what one row of data represents.

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Common mistake

Do not call all city residents the target. The study explicitly aims at registered city voters, matching the registration-list frame.

Solution walkthrough video