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What does an interval estimate leave uncertain?

An interval’s interpretation depends on the procedure and its assumptions.

Statistics & dataTopic · Selected readingSome background helpful
Background and goal

Try the short introduction first, or bring equivalent reading experience. Obtain the specified text before beginning the longer reading.

Compare two hypothetical estimates with the same centre and different intervals; explain what additional information you need.

Useful preparation

Start here if the background is new. Equivalent experience is enough.

Your pathway

5 steps · 14 hours
  1. 01

    Locate the reading

    0.25h · week 1
    Reading notes and task
    First fifteen minutesCheck the edition or article version and locate the passages below. Write the question you want the reading to resolve.
    Your outputEdition and passage record
  2. 02

    Study the opening

    4h · week 1
    Introductory Statistics 2e

    OpenStax · book

    Chapters 7–8, sampling distributions and confidence intervals; introductory examples

    Free full text

    Open the reading
    Reading notes and task

    Introductory Statistics 2e. An interval’s interpretation depends on the procedure and its assumptions.

    Try thisRead Chapters 7–8, sampling distributions and confidence intervals; introductory examples. Reconstruct the central argument using premises and a conclusion.
    Your outputArgument reconstruction
    Check your understanding

    Answer this question in your own words: What does an interval estimate leave uncertain?

    Hint

    Name the claim, then explain why a reader might accept it.

    Compare with an example answer

    An interval’s interpretation depends on the procedure and its assumptions.

    What to look for

    • States a claim that addresses the question
    • Connects the claim to a passage or observation
    • Separates the author’s argument from personal agreement

    Common mistake: Summarising a biography instead of explaining the argument.

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  3. 03

    Read for contrast

    5h · week 2
    Introductory Statistics 2e

    OpenStax · book

    Chapters 7–8, sampling distributions and confidence intervals; introductory examples

    Free full text

    Open the reading
    Reading notes and task

    Introductory Statistics 2e. An interval’s interpretation depends on the procedure and its assumptions.

    Try thisRead Chapters 7–8, sampling distributions and confidence intervals; introductory examples. Compare two passages that put pressure on your initial interpretation.
    Your outputTwo-passage comparison
  4. 04

    Develop an example

    3h · week 3
    Reading notes and task
    Try thisCompare two hypothetical estimates with the same centre and different intervals; explain what additional information you need.
    Your outputWorked example
    Check your understanding

    What would make your activity a convincing example?

    Hint

    Compare two hypothetical estimates with the same centre and different intervals; explain what additional information you need.

    Compare with an example answer

    A useful response carries out the task: Compare two hypothetical estimates with the same centre and different intervals; explain what additional information you need. It records the observation or passage used and explains how it bears on the question.

    What to look for

    • Completes the specific task
    • Shows evidence or reasoning rather than only a conclusion
    • Identifies an alternative explanation or reading

    Common mistake: Presenting an opinion without showing the example it rests on.

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  5. 05

    Write a considered response

    1.75h · week 4
    Reading notes and task
    Try thisWrite a response to “What does an interval estimate leave uncertain?” that uses both passages and tests its own conclusion. A confidence interval does not assign a probability to every fixed parameter value.
    Your outputReasoned response with references
    Check your understanding

    What is one conclusion this reading does not establish?

    Hint

    Test the boundary: A confidence interval does not assign a probability to every fixed parameter value.

    Compare with an example answer

    A confidence interval does not assign a probability to every fixed parameter value.

    What to look for

    • States a specific limit
    • Explains why the reading does not warrant the stronger conclusion
    • Distinguishes a limitation from dismissing the work

    Common mistake: Treating a useful interpretation as an unrestricted fact.

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All 1 resources

Background, different viewpoints, and further reading.

  • Introductory Statistics 2e

    OpenStaxbookcore

    An interval’s interpretation depends on the procedure and its assumptions.

    Chapters 7–8, sampling distributions and confidence intervals; introductory examples