Octopus Paul in 2010 predicted $8$ matches out of $8$ correctly during the football World Cup. Assume that Paul predicts the winner of a match with probability $p$, assume also that a match can not end with draw. You wish to investigate whether Paul has exceptional prediction abilities by using a statistical test, What are the relevant hypothesis?
1) $H_0:p=0.5$, $H_1:p>0.5$
2) $H_0:p<1$, $H_1:p=1$
3) $H_0:p=1$, $H_1:p<1$
4) $H_0:p>0.5$, $H_1:p=0.5$
I think that the correct one is number 4 because we investigate if the probability of prediction is higher that 0.5 (random selection) it's right?