Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 38 / 4 / b / Solution

Now $p_A=2/3$, $p_B=1/2$, so $\bar{p}=7/12$, $\Delta =1/6$, $v_0=35/72$ and $v_1=17/36$. The same sample size calculation givesAt $\alpha =0.05$, the illustrative two-sided total is $2\times 137=274$; the one-sided total is $2\times 108=216$. The smaller difference needs roughly four times the size: its squared magnitude is a quarter of the previous one, while the variance factors change comparatively little.