For a die, let p p\,p be the probability of rolling a 6. Polly suspects that p≠0.4p\ne0.4p=0.4. The die will be rolled 20 times.
Find the probability of exactly five 6s under p=0.4p=0.4p=0.4.
State suitable hypotheses.
Find a two-tailed critical region for a 10% test, with the probability in each tail less than 0.05.
Find the actual significance level.
Polly obtains eleven 6s. State the conclusion.
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.