Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
The local council says that the mean number of accidents each year on one specific road is $0.8$. Jane argues that the actual mean is above $0.8$. She examines the records from a random sample of $3$ recent years and discovers that there were $5$ accidents in total across those $3$ years.
(a(i))[1]
Suppose that the yearly number of accidents is modelled by a Poisson distribution. Write down the null and alternative hypotheses for a test of Jane’s claim.
(a(ii))[4]
Carry out a test at the $5\%$ significance level to decide whether Jane’s claim can be supported.
(b)[1]
Jane notices that the yearly number of accidents has been rising gradually in recent years. State how this could influence the validity of the test used in part (a)(ii).
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use $H_0: \lambda = 2.4$ and $H_1: \lambda > 2.4$” …