Billy plays darts. He assumes that each throw is independent of every other throw, and he knows from past experience that the probability of hitting the bullseye is 0.2.
Billy believes he has improved, so that the probability of hitting the bullseye is now greater than 0.2. He throws 20 darts, and 6 hit the bullseye.
Stating your hypotheses clearly, test Billy's belief at the 5% significance level.