 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ib/paper-2/6h/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Under the null hypothesis of independence between treatment and outcome, the expected counts in each treatment row are one half of the column totals:

(10, 20, 10, 10) .

X^{2} = 2 (\frac{( 14 - 10 ) ^{2}}{10} + \frac{( 21 - 20 ) ^{2}}{20} + \frac{( 10 - 10 ) ^{2}}{10} + \frac{( 5 - 10 ) ^{2}}{10}) = 8.30 .

(2 - 1) (4 - 1) = 3.

At the 5% level the critical value is

7.81

. Since

8.30 > 7.81

, we reject the null hypothesis and find statistically significant evidence that the drug and placebo have different effects.

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