Card 1 of 20
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Prompt
What is a population?
Define it from the intended conclusion.
Answer
The complete group a study aims to describe.
Example
All students enrolled at a school.
MathChapter 8: Statistics
Flashcards
Populations, Samples, and Random Selection Flashcards
Twenty concise cards on population and sample roles, random selection, bias, proportional estimates, size, variability, and inference.
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Card 2 of 20
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Prompt
What is a sample?
It is measured, not merely targeted.
Answer
The subset from which data are collected.
Example
The \(200\) selected students.
Card 3 of 20
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Prompt
What is a census?
No sampling subset remains.
Answer
Data collection from every population member.
Example
Survey all \(1{,}200\) employees.
Card 4 of 20
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Prompt
What is a population parameter?
It belongs to the population.
Answer
A numerical characteristic of the full population.
Example
The true proportion of all voters supporting a proposal.
Card 5 of 20
EasyStudy card 5
Prompt
What is a sample statistic?
It can estimate a parameter.
Answer
A numerical summary calculated from sample data.
Example
The proportion supporting the proposal in a random sample.
Card 6 of 20
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Prompt
What is random selection?
Use a complete frame when possible.
Answer
A chance-based method intended to avoid systematically favoring population members.
Example
Randomly draw IDs from the full roster.
Card 7 of 20
MediumStudy card 7
Prompt
What is a convenience sample?
Ease can create undercoverage.
Answer
A sample chosen because members are easy to reach.
Example
Survey people nearest the entrance.
Card 8 of 20
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Prompt
What is voluntary-response bias?
Strong opinions may be overrepresented.
Answer
People who choose to respond may differ from those who do not.
Example
An open website poll.
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Prompt
What is undercoverage?
Inspect the sampling frame.
Answer
Some population groups have little or no chance to enter the sample.
Example
A phone list omits residents without listed numbers.
Card 10 of 20
MediumStudy card 10
Prompt
What is sampling variability?
Random does not mean identical.
Answer
Natural differences among statistics from different random samples.
Example
Two random polls may report \(48\%\) and \(51\%\).
Card 11 of 20
MediumStudy card 11
Prompt
What is the sample-proportion formula?
Divide sampled successes by sample size.
Answer
\(\hat{p}=x/n\).
Example
\(42/150=0.28\).
Card 12 of 20
MediumStudy card 12
Prompt
How is a population count estimated from a sample proportion?
Scale the rate, not the raw sample count.
Answer
Multiply by population size: \(\hat{p}N\).
Example
\(0.28(2500)=700\).
Card 13 of 20
MediumStudy card 13
Prompt
Is a scaled sample count exact?
Precise arithmetic does not create a census.
Answer
No. It is an estimate subject to sampling variability and method quality.
Example
Say ‘about \(700\).’
Card 14 of 20
MediumStudy card 14
Prompt
What does increasing a good random sample generally improve?
It does not guarantee exactness.
Answer
It reduces sampling variability and stabilizes the estimate.
Example
A random sample of \(800\) is generally steadier than one of \(80\).
Card 15 of 20
MediumStudy card 15
Prompt
Can a large sample fix selection bias?
Size and representativeness solve different problems.
Answer
No.
Example
A huge voluntary poll may remain biased.
Card 16 of 20
MediumStudy card 16
Prompt
What should be audited before calculating an estimate?
Method before arithmetic.
Answer
Population, sampling frame, selection method, and missing groups.
Example
Check whether every target group can be selected.
Card 17 of 20
HardStudy card 17
Prompt
Why can equal-sized random samples from two large populations have similar reliability?
Do not compare percentages alone.
Answer
Sampling variability depends strongly on random sample size and quality, not just sampled percentage, at this source level.
Example
Samples of \(300\) from two very large populations.
Card 18 of 20
HardStudy card 18
Prompt
What is generalizability?
It depends on selection and coverage.
Answer
The degree to which sample results can reasonably describe the target population.
Example
A school-only sample cannot automatically describe a city.
Card 19 of 20
HardStudy card 19
Prompt
How is a stated margin applied to a sample proportion?
Write \(\hat{p}\pm m\).
Answer
Add and subtract it from the estimate.
Example
\(0.42\pm0.04\) gives \(0.38\) to \(0.46\).
Card 20 of 20
HardStudy card 20
Prompt
What terminology distinction prevents a common trap?
Keep population and sample roles separate.
Answer
A population parameter is the target characteristic; a sample statistic is the calculated estimate source.
Example
\(\hat{p}\) estimates a population proportion.
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