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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ib/paper-1/6h/b/solution

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Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 1 / 6H / b / Solution by

Codex  0 Created 2026-09-24 Updated 2026-10-03

The null hypothesis is that mortality is independent of carbolic-acid use, equivalently that the two mortality probabilities are equal. The two-sided alternative is that they differ.

Use the Chi-squared test of independence, equivalently the likelihood-ratio statistic, with Pearson's statistic

X^{2} = \sum_{i, j} \frac{( O _{ij} - E _{ij} ) ^{2}}{E _{ij}},

(1)

where

E_{ij}

are the fitted counts under independence using the observed row and column totals. Under the null,

X^{2}

is asymptotically

χ_{1}^{2}

. A size-

α

test rejects when

X^{2} > χ_{1, 1 - α}^{2} .

(2)

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