 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2002/iii/paper-37/3/ii/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

Two distinct issues are:

Exposure measurement and comparability. Infectious-dose estimates can have substantial error, and consumption categories may differ in infectivity or processing. If the assumed cohort exposure ratio is wrong, the expected allocation used in the goodness-of-fit test is wrong. The calendar distribution within the aggregated exposure period also matters for how many onsets have matured by the observation date.
Ascertainment of outcomes. Clinical recognition, diagnostic testing, reporting and competing mortality may differ between cohorts. Unequal detection probabilities can alter the observed onset ratio even with equal biological susceptibility and incubation periods.

Thus the comparison must account for uncertainty in both its exposure denominator and its observed-disease numerator; a very small sampling p-value does not remove those model uncertainties.

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