A roadside study found that 62% of petrol cars in its sample had CO2 _2\,2 emissions above 150 g/km. The study sampled cars from three regions during one year.
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 the information about the original study, give one reason why Sam's conclusion cannot be applied to all petrol cars registered in England.
40 exam-style questions on WJEC A Level Maths 2.5 Statistical hypothesis testing, covering 2.5.1 Statistical hypothesis testing, 2.5.2 Statistical hypothesis testing, 2.5.3 Statistical hypothesis testing, 2.5.4 Statistical hypothesis testing, and 2.5 Statistical hypothesis testing. Each one has a worked solution and a mark scheme showing where the marks go.