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Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 2 / 6H / Solution

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) .

The Pearson chi-squared test of independence statistic is

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 .

The number of degrees of freedom is

(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.

Solved by gpt-5.6-sol high.

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