Give Every Roster Member a Selection Chance
A simple random sample can be created by selecting distinct random identifiers from a complete roster.
About 20 minutes, plus any extended practice
Supplied materials
- Paper or a browser scratch area; a calculator is optional unless rounding is requested.
- Supplied teaching case: A fictional school has 40 students on one roster. Which plan is a simple random sample of 20 students? Candidate answers: (A) Ask 20 members of the chess club (B) Ask the first 20 students entering the library (C) Assign every roster member a number; randomly select 20 different numbers (D) Choose 20 students whose names you recognize.
- Independent check inputs: A fictional school has 60 students on one roster. Which plan is a simple random sample of 20 students? Candidate answers: (A) Ask 20 members of the chess club (B) Ask the first 20 students entering the library (C) Assign every roster member a number; randomly select 20 different numbers (D) Choose 20 students whose names you recognize.
Learn the idea
A complete population, a selected sample and a probability model are different sources of information. Sampling supports estimates, observed trial counts support experimental proportions, and explicit independence permits multiplication of model probabilities. A simple random sample can be created by selecting distinct random identifiers from a complete roster. Convenience selection can overrepresent groups tied to the selection location or activity.
Here is the method on the supplied teaching case. Random selection from the complete roster gives each roster member the same selection chance. Convenience or one-club samples can underrepresent other students.
Random selection requires an actual procedure rather than a claim that volunteers seem varied. A complete roster and selection without duplicate identifiers matter; the sample does not automatically include every subgroup in equal counts.
- Write or sketch the supplied teaching case, labeling its quantities and restrictions.
- Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
- Solve the independent check with its changed inputs before revealing feedback.
- Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.
See the method in action
Teaching case: A fictional school has 40 students on one roster. Which plan is a simple random sample of 20 students? Candidate answers: (A) Ask 20 members of the chess club (B) Ask the first 20 students entering the library (C) Assign every roster member a number; randomly select 20 different numbers (D) Choose 20 students whose names you recognize. Solution: Random selection from the complete roster gives each roster member the same selection chance. Convenience or one-club samples can underrepresent other students. The final answer is Assign every roster member a number; randomly select 20 different numbers. Random selection requires an actual procedure rather than a claim that volunteers seem varied. A complete roster and selection without duplicate identifiers matter; the sample does not automatically include every subgroup in equal counts.
Check your reasoning
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Helpful tips
- A simple random sample can be created by selecting distinct random identifiers from a complete roster.
- Random selection requires an actual procedure rather than a claim that volunteers seem varied.
See the answer and explanation
Assign every roster member a number; randomly select 20 different numbers
Random selection from the complete roster gives each roster member the same selection chance. Convenience or one-club samples can underrepresent other students.
Take it further
Changed-input task: A fictional school has 180 students on one roster. Which plan is a simple random sample of 20 students? Candidate answers: (A) Ask 20 members of the chess club (B) Ask the first 20 students entering the library (C) Assign every roster member a number; randomly select 20 different numbers (D) Choose 20 students whose names you recognize. Show the mathematical reason, not only the selected answer. Expected result: Assign every roster member a number; randomly select 20 different numbers. Random selection from the complete roster gives each roster member the same selection chance. Convenience or one-club samples can underrepresent other students.
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More practice: try new cases
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