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Confidence intervals

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Useful for: AP® Statistics IB Math AI HL

Learn it A confidence interval is estimate ± margin of error. For a proportion: p̂ ± z*√(p̂(1 − p̂)/n); for a mean (σ known): x̄ ± z*σ/√n. z* = 1.96 for 95%, 1.645 for 90%, 2.576 for 99%. '95% confident' means the method captures the true value 95% of the time.

Example: In a poll, 540 of 1000 support a plan. 95% interval?

  1. p̂ = 0.54. ME = 1.96√(0.54 × 0.46/1000) ≈ 0.031.
  2. 0.509 to 0.571.

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