Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 207 / 3 / c

Table of contents
- Solution c

Solution

Let

n

be the sample size in each arm,

π_{1 A} = π_{0} + δ_{A}

, and

\overset{π}{ˉ}_{A} = (π_{1 A} + π_{0}) /2

. Solving the normal-approximation power equation gives

n = \frac{[ z _{1 - α} 2 π ˉ _{A} ( 1 - π ˉ _{A} ) + z _{1 - β} π _{1 A} ( 1 - π _{1 A} ) + π _{0} ( 1 - π _{0} ) ] ^{2}}{δ _{A}^{2}},

rounded upward. The total sample size is

2 n

.

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