A shuffling machine
Twenty fresh packs are shuffled. Seventeen have a red card on top. Test whether the top card is still equally likely to be red or black, against the alternative that red is more likely than 1/2. The one-sided binomial p-value is 0.00174.
Worked answer (click to show)
H_0:p=1/2 against H_1:p>1/2, with X\sim\operatorname{Bin}(20,p) the number of red top cards. The observed value is 17. The p-value \mathbb{P}(X\ge 17\mid p=1/2)=0.00174, so the machine is not consistent with a fair top card.