People use animals to predict outcomes of sporting events and elections mostly by having the animals pick between two containers of food, each representing one of the two teams or the two candidates involved. Probably the most famous of these is Paul the Octopus from Germany who was correct in all eight of his predictions for the 2010 World Cup. Do his results provide strong evidence that Paul is doing something other than randomly guessing and perhaps has some psychic power? 

a. If we will let π be Paul’s probability of picking the winning team, what are the null and alternative hypotheses in symbols? 

b. Use the One Proportion applet to find a p-value. Interpret this p-value in the context of the study. 

c. Write out a conclusion in the context of the research question. 

d. As was stated earlier, many animals are used to predict outcomes of sporting events with most of them not doing any better than random chance and therefore not getting much publicity. Paul made the news because he was so accurate. Do you think it is surprising that some animal would be very successful like Paul was? Explain.