Question

During the 2010 World Cup tournament, Paul the Octopus (in a German aquarium) became famous for correctly predicting the winner in all 8 games it was asked to predict. (Two containers of food were lowered into Paul’s tank, each with a flag of the opposing teams. He made a selection by choosing which container to eat from. Is this evidence that Paul has psychic powers and can choose correctly more than half the time? State the null and alternative hypotheses: What is Paul’s sample proportion? We want to see how unlikely it is to have an 8 for 8 record if Paul is just randomly guessing. We can simulate this with a coin! Each coin flip represents a guess between two teams, with "heads" standing for a correct guess and "tails" for incorrect. Why does this method work for assuming the null hypothesis is true?

Answer 1

Step-by-step explanation:

1.

let's define p as the proportion of all correct guesses made by the octopus paul.

null hypothesis

h0: p = 0.5

alternative hypothesis

h1: p > 0.5

2.

we are to get paul's sample proportion

= p^ = 8/8 = 1

3.

in this last question we are to state why this method works for assuming that null hypothesis is true.

the reason is that the null hypothesis was stated as p = 0.5 and we know that a coin would land as head 50% or half of the time.

thank you!