STAT HELP Question

Question

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 semi-final 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.1 Does Paul have psychic power? In other words, is an 8 for 8 record significantly better than just guessing?

Round the p-value to three decimal places.

Answer 1

Assuming he was guessing the probability of getting each correct is .5 with 8 trials. There are 2 ways to find the probability of getting all 8 correct

.5 x .5 x .5 … = (.5)^8

oruse a binomial distribution since there are a fixed number of trials binompdf(8, .5, 8)

both answers give you .0039. Since this probability is less than 5% it cannot happen by chance alone so therefore Paul DOES have psychic powers since it is statistically significant.