Billy hits a dartboard bullseye independently with probability 0.2.
Find the probability that at least 3 of 9 darts hit the bullseye. Billy then believes he has improved after six of his next 20 darts hit. For part (b), use H0:p=0.2H_0:p=0.2H0:p=0.2, H1:p>0.2 H_1:p>0.2\,H1:p>0.2 and X∼B(20,0.2)X\sim B(20,0.2)X∼B(20,0.2) under H0H_0H0.
Calculate the exact p-value.
State the decision at the 5% level and give a conclusion in context.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.