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

A 95% confidence interval for a normal mean based on a sample of 25 observations with unknown variance is computed using the t distribution. Which statement about the interval is correct?

The t interval is wider than the z interval with the same s. The t(24) critical value, about 2.064, exceeds 1.96 because the t distribution has heavier tails, reflecting the extra uncertainty from estimating the variance.

  1. AIt is wider than the z interval with the same s because t(24) has heavier tails than the normalCorrect
  2. BIt is narrower than the z interval with the same s because s is estimated
  3. CIt has the same width as the z interval for any sample size
  4. DIts width does not depend on the sample variance
  5. It contains the sample mean only 95% of the time

Explanation

The t(24) critical value of about 2.064 exceeds 1.96, so the interval is wider for the same s and n. This allows for the extra uncertainty from estimating the variance. Width depends on s, and the interval always contains the sample mean as its midpoint.

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