It is known that 75% of the diesel cars registered in the earlier of the two years covered by the AQA Large Data Set have CO emissions of less than 0.3 g/km.
Jo wants to investigate whether the proportion of diesel cars with CO emissions of less than 0.3 g/km has changed in the later year. She will carry out a hypothesis test at the 10% significance level, with a probability of at most 0.05 in each tail, using a random sample of 30 diesel cars registered in the later year.
State suitable null and alternative hypotheses for Jo's test.
Using a 10% significance level, find the critical region for Jo's test.
In her random sample, Jo finds 22 cars with CO emissions of less than 0.3 g/km. State Jo's conclusion in context.
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.