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📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 An epidemiologist estimates that a vaccine reduces infection risk by 75%. In a trial with 10,000 vaccinated and 10,000 unvaccinated, 200 vaccinated and 500 unvaccinated get infected. Do the numbers are consistent with the expected risk reduction? (Calculate observed vs expected.)

📌 Expected infections in vaccinated if 75% reduction:

📌 Unvaccinated infection rate = \( \frac{500}{10,000} = 5\% \)

📌 Expected risk: \( 5\% \times (1 - 0.75) = 1.25\% \)

📌 Expected infections: \( 0.0125 \times 10,000 = 125 \)

📌 Observed: 200

📌 Observed rate: \( \frac{200}{10,000} = 2\% \)

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