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IAI Actuarial Core Principles · Actuarial Statistics · Confidence intervals and prediction intervals

Which statement about a 95% confidence interval (L, U) for a parameter θ, calculated from a single sample, is correct?

Before the sample is drawn, the random interval has probability 0.95 of containing the fixed parameter. After calculation, the interval either contains it or not, so the 0.95 describes the procedure's long-run coverage rather than a probability about the parameter.

  1. AThe probability is 0.95 that θ lies in the calculated interval (L, U).
  2. B95% of the sample observations lie within (L, U).
  3. CBefore sampling, the random interval has probability 0.95 of containing θ.Correct
  4. Dθ is a random variable with 95% of its distribution inside (L, U).
  5. A 99% interval from the same data will be narrower.

Explanation

The confidence level refers to the random interval before data are observed: P(L(X) < θ < U(X)) = 0.95. Once computed, the interval either contains the fixed θ or it does not. A higher confidence level gives a wider interval, not narrower.

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