Polly suspects that a die is biased. The probability of the die landing on 6 is believed to be 0.4, and Polly thinks this probability has changed. The die is to be rolled 20 times, and X X\,X is the number of sixes obtained.
Write down the hypotheses Polly should use.
Using a 10% significance level, find the critical region for a two-tailed test, with a probability of at most 0.05 in each tail.
Find the actual significance level of a test based on this critical region.
Polly rolls the die 20 times and obtains 11 sixes. Comment on Polly's suspicion.
162 exam-style questions on AQA A Level Maths 2.5 O: Statistical hypothesis testing, covering 2.5.1 Language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, and 2.5.3 Hypothesis test for a Normal mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.