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Mathematics · University

Intervals, tests and uncertainty

A value computed from sample data to approximate a population quantity.

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Prerequisites

High-school algebra.

Study notes

Estimate

A value computed from sample data to approximate a population quantity.

Confidence interval

A range produced by a method designed to capture a population parameter at a stated long-run rate under assumptions.

Null hypothesis

A specified reference claim used in a significance test.

P-value

A probability, under the null model, of data at least as incompatible with that model as the observed result by the test statistic.

Worked examples

Which term best matches this description: A value computed from sample data to approximate a population quantity.

Estimate is the matching concept in this lesson.

Estimate

Which term best matches this description: A range produced by a method designed to capture a population parameter at a stated long-run rate under assumptions.

Confidence interval is the matching concept in this lesson.

Confidence interval

Check your understanding

  1. Which concept would you apply first in a situation where a specified reference claim used in a significance test.

    1. Estimate
    2. P-value
    3. Confidence interval
    4. Null hypothesis

  2. Name the concept described as: A probability, under the null model, of data at least as incompatible with that model as the observed result by the test statistic.

  3. Which statement about Estimate is most accurate?

    1. A probability, under the null model, of data at least as incompatible with that model as the observed result by the test statistic.
    2. A value computed from sample data to approximate a population quantity.
    3. A range produced by a method designed to capture a population parameter at a stated long-run rate under assumptions.
    4. A specified reference claim used in a significance test.

  4. Explain one important difference between Estimate and Confidence interval.

Answers and marking guidance

Answers and marking notes
  1. Null hypothesis

    The scenario directly calls for Null hypothesis.

  2. P-value

    The intended concept is P-value.

  3. A value computed from sample data to approximate a population quantity.

    The definition in the lesson notes gives the required condition.

  4. Estimate: A value computed from sample data to approximate a population quantity. Confidence interval: A range produced by a method designed to capture a population parameter at a stated long-run rate under assumptions.

    Credit a clear distinction using both definitions and an appropriate example if supplied.

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