 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ib/paper-3/18h/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Under

H_{0}

n \overline{X} \sim N (0, 1) .

Let

z_{1 - α /2} = Φ^{- 1} (1 - α /2)

. The standard two-sided level-

α

test rejects exactly when

∣ n \overline{X} ∣ > z_{1 - α /2} .

For the observed value

\overline{X} = \overline{x}

p (\overline{x}) = 2 [1 - Φ (n ∣ \overline{x} ∣)] .

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