In the 2010 World Cup, Paul the Octopus (in a German aquarium) became famous for being correct in all eight of the predictions it made, including predicting Spain over Germany in a semifinal match. Before each game, two containers of food (mussels) were lowered into the octopus’s tank. The containers were identical, except for country flags of the opposing teams, one on each container. Whichever container Paul opened was deemed his predicted winner. Does Paul have psychic powers? In other words, is an 8-for-8 record significantly better than just guessing?

(a) State the null and alternative hypotheses.

(b) Simulate one point in the randomization distribution by flipping a coin eight times and counting the number of heads. Do this five times. Did you get any results as extreme as Paul the Octopus?

(c) Why is flipping a coin consistent with assuming the null hypothesis is true?