Before a drug‑prevention programme was introduced, a survey found that $12\%$ of youths aged 15-19 in a community used illicit drugs. After two years, a follow‑up survey of $500$ participants in the programme showed an $8\%$ usage rate, while a comparable control group of $500$ youths (who did not receive the programme) showed an $11\%$ usage rate.

(a) Calculate the absolute risk reduction (ARR) and the relative risk reduction (RRR) achieved by the programme.

(b) Using a chi‑square test for independence at the $5\%$ significance level, determine whether the difference in usage rates is statistically significant. State the chi‑square value, the critical value, and your conclusion.

Question

Before a drug‑prevention programme was introduced, a survey found that $12\%$ of youths aged 15-19 in a community used illicit drugs. After two years, a follow‑up survey of $500$ participants in the programme showed an $8\%$ usage rate, while a comparable control group of $500$ youths (who did not receive the programme) showed an $11\%$ usage rate.

(a) Calculate the absolute risk reduction (ARR) and the relative risk reduction (RRR) achieved by the programme.

(b) Using a chi‑square test for independence at the $5\%$ significance level, determine whether the difference in usage rates is statistically significant. State the chi‑square value, the critical value, and your conclusion.

Accepted Answer

ARR = 3 %; RRR ≈ 27.3 %; chi‑square = 2.617 (critical 3.841) → not statistically significant at the 5 % level

Neco Model Questions Vol1 2025 Civic Education Question 30

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