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.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.