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IAI Actuarial Core Principles · Actuarial Statistics · Hypothesis testing and goodness of fit

For a test of H0: μ = 100 against H1: μ ≠ 100, the observed test statistic is z = −1.75 from a standard normal reference distribution. Given Φ(1.75) = 0.9599, what is the p-value and the conclusion at the 5% level?

For a two-sided test the p-value is twice the tail area, 2 × 0.0401 = 0.0802. Because this exceeds 0.05, there is insufficient evidence to reject the null hypothesis at the 5% level.

  1. A0.0401; do not reject H0
  2. B0.0802; do not reject H0Correct
  3. C0.0401; reject H0
  4. D0.0802; reject H0
  5. 0.9599; do not reject H0

Explanation

A two-sided test doubles the tail probability: 2 × (1 − 0.9599) = 0.0802. Since 0.0802 > 0.05, H0 is not rejected. The value 0.0401 is the one-sided p-value, which is wrong for a two-sided alternative.

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