A CI procedure with 95% confidence captures the parameter

Answer: About 95% of the time in repeated sampling Frequentist guarantee: 95% of intervals capture the true parameter in the long run.

Answer: σ is known Most real cases use t because σ is rarely known.

Use a paired t when data are

Answer: Pairs of related observations (matched/repeated) Pairing reduces variability by controlling for individual differences.

AP Statistics · Topic 7.10

Skills Focus: Selecting, Implementing, and Communicating Inference Procedures Practice

Part of Inference for Quantitative Data: Means.

Practice questions

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Sample questions

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Sample 1difficulty 3/5
$A CI procedure with 95% confidence captures the parameter$
- A
  $About 95% of the time in repeated sampling$
  check_circle
- B
  $Always$
- C
  $Only if H₀ is true$
- D
  $Never if biased$
Why
$Frequentist guarantee: 95% of intervals capture the true parameter in the long run.$
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Sample 2difficulty 3/5
$Use z (not t) when$
- A
  $Always$
- B
  $n < 30 always$
- C
  $σ is known$
  check_circle
- D
  $σ is unknown$
Why
$Most real cases use t because σ is rarely known.$
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Sample 3difficulty 4/5
$Use a paired t when data are$
- A
  $Categorical$
- B
  $Pairs of related observations (matched/repeated)$
  check_circle
- C
  $Two unrelated samples$
- D
  $One sample only$
Why
$Pairing reduces variability by controlling for individual differences.$
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Sample 4difficulty 4/5
$Comparing the same group's heart rate before and after exercise uses$
- A
  $Two-sample t$
- B
  $Chi-square$
- C
  $Paired t (matched)$
  check_circle
- D
  $Two-sample z$
Why
$Same individuals measured twice \to paired/matched.$
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Sample 5difficulty 4/5
$A 95% CI for μ that excludes 0 implies$
- A
  $Always fails to reject$
- B
  $Two-sided test of H₀: μ = 0 rejects at α = 0.05$
  check_circle
- C
  $Sample bias$
- D
  $p-value > 0.05$
Why
$CI exclude null value \Leftrightarrow test rejects at the corresponding level.$
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