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

For a sample of n from a normal distribution with unknown mean and variance, which statement about the 95% confidence interval for μ based on the t distribution is correct?

The t interval is wider than the z interval using the same sample standard deviation, because the t distribution has heavier tails and its critical value exceeds 1.96. It allows for estimating the variance and is exact for normal samples.

  1. AIt is wider than the interval using z with the same s, because t has heavier tailsCorrect
  2. BIt is narrower than the z interval with the same s
  3. CIts width does not depend on the sample variance
  4. DIt requires the population variance to be known
  5. Its coverage is exactly 95% only for large n regardless of normality

Explanation

The t critical value exceeds 1.96 for any finite degrees of freedom, so with the same s the t interval is wider. Its width depends on s, and it is exact for normal data at any n.

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