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AP® Statistics · Unit 4 · Topic 4.3

Justifying a Claim Based on a Confidence Interval for a Mean: Topic Checklist (Statistics 4.3)

Specific “I can…” statements for interpreting t-intervals and confidence levels and judging claims about a mean or mean difference, each linked to the guide section and practice question.

Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions.

Understanding

  • I can explain why one calculated t-interval may or may not contain the population mean, and why the widths of t-intervals vary. (Guide: “What a t-interval does and does not tell you”; Figure 1)
  • I can explain why “there is a 95% probability that μ is in this interval” is wrong. (Guide: “Common misconceptions”; Practice Q1)
  • I can explain why a plausible value is not a proved value, and why “0 is in the interval” does not mean “no difference”. (Guide: “Using an interval to justify a claim”; Practice Q3)

Skills

  • I can interpret a t-interval for μ in context, with the level, both endpoints, units and the population. (Guide: Worked example 1; Practice Q1, Q5)
  • I can interpret a t-interval for μd, stating the order of subtraction. (Guide: Worked example 2; Practice Q7)
  • I can interpret a confidence level as the long-run capture rate in repeated random samples of the same size. (Guide: “Interpreting the confidence level”; Practice Q5(c))
  • I can predict how raising or lowering the confidence level changes t*, the margin of error and the width. (Guide: Worked example 3; Practice Q2, Q6)
  • I can predict how changing n changes the standard error, t* and the width, using the 1/√n rule. (Guide: Worked example 3; Practice Q4)
  • I can recover x̄, the margin of error and s from a reported interval. (Practice Q6, Q7(d))

Reasoning

  • I can decide whether an interval gives convincing evidence for or against a claimed value of μ. (Guide: Worked example 1; Practice Q5(d))
  • I can use 0 and the sign of a matched-pairs interval to judge a claim of a difference, in context. (Guide: Worked example 2; Practice Q3, Q7(c))
  • I can explain why the same data can support different conclusions at different confidence levels. (Guide: Worked example 1 check; Practice Q6)

All ticked? Move on to Topic 4.4, Setting Up a Test for a Population Mean or Population Mean Difference, or return to the course roadmap.

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