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Survey responses 5k contain 2k reports in seconds although the question asked minutes. Is direct pooling valid?

Read the idea, work independently, then explain what changed.

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高一必修 第二册(A版).pdf · 9.3 · PDF 227 / printed page 220

Revisit first: Estimating a population from a sample

TOPIC 01

Statistical case study

Build understanding of statistical case study through definitions, contrasting cases and justified applications.

What you will be able to explain

  • Use statistical case study to state a justified conclusion.
  • Connect representations and justify the steps, including boundary cases.
  • Explain a solution and apply the idea to a changed situation.

Try it. Leave your reasoning visible.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

Survey responses 5k contain 2k reports in seconds although the question asked minutes. Is direct pooling valid?

k=3k=3
  • Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
State the survey question, population, sampling and measurement rules before drawing a conclusion.
Hint 2
Check definitions and units before summary statistics.
Worked solution
  1. State the survey question, population, sampling and measurement rules before drawing a conclusion.

  2. Calculate or simplify this relation.

    1 minute=60 seconds1\text{ minute}=60\text{ seconds}
  3. Cleaning decisions should remain documented, not silently delete difficult cases.

No. Convert compatible units and flag ambiguous responses before analysis.

Checks and common pitfalls: Cleaning decisions should remain documented, not silently delete difficult cases.

Reasoning checklist · self / teacher assessment
  • State the relevant definition, condition or model.
  • Show a valid calculation, proof or counterexample.
  • Interpret the conclusion with its restrictions.

Think first. Reveal a hint when the class is ready.

Focus on one question

Teacher preparation and assessment

Question sequence

  • What must be true before using the main rule for statistical case study?
  • Which representation makes this task easier, and why?
  • Change one assumption. Does the conclusion survive?

Board plan

  • Use statistical case study to state a justified conclusion.
  • Full investigation: Define the target, collect compatible data, analyze and report limitations.
  • Ethical reporting: Use anonymous classroom data and preserve uncertainty and exclusions.
  • Close with: conditions → representation → reasoning → check.

Anticipated thinking

  • Expected reasoning: Define the target, collect compatible data, analyze and report limitations.
  • Expected reasoning: Use anonymous classroom data and preserve uncertainty and exclusions.
  • Expected correction: A statistical association alone is not a causal conclusion.

Assessment checklist

  • 1: identify the givens and required quantity.
  • 1: choose a valid definition, representation or method.
  • 1: present connected, correct reasoning.
  • 1: check conditions and explain the result.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗