Billy plays darts. He assumes that each dart throw is independent and he knows from past experience that the probability of hitting the bullseye is 0.2
Billy throws 9 darts. Calculate the probability that at least 3 of the darts will hit the bullseye.
Billy believes he has improved and the chance of hitting the bullseye is greater than 0.2. He throws 20 darts and 6 hit the bullseye. Stating your hypotheses clearly test, at the 5% level of significance, whether or not there is evidence to support Billy's belief.
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.