It is known that 62% of the petrol cars in the AQA Large Data Set have CO2 _2\,2 emissions above 150 g/km.
Sam takes a random sample of 28 petrol cars from a garage and wishes to test, at the 10% significance level with a probability of at most 0.05 in each tail, whether the proportion of petrol cars with CO2 _2\,2 emissions above 150 g/km differs from 62%.
Find the critical region for Sam's test.
Find the actual significance level of a test based on this critical region.
In Sam's sample, 23 of the cars have CO2 _2\,2 emissions above 150 g/km. State Sam's conclusion in context.
Using your knowledge of the Large Data Set, give one reason why Sam's conclusion cannot be applied to all petrol cars registered in England.
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.