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Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 3 / 18H / a / Solution

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}

, its two-sided Gaussian p-value is

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

Solved by gpt-5.6-sol high.

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