The local council claims that the average number of accidents per year on a particular road is 0.8. Jane claims that the true average is greater than 0.8. She looks at the records for a random sample of 3 recent years and finds that the total number of accidents during those 3 years was 5.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [B1] H₀: λ = 2.4 H₁: λ > 2.4 Accept λ or μ Accept 2.4 or 0.8 (per year)
2. [M1] 1 – e⁻²·⁴(1 + 2.4 + 2.4²/2 + 2.4³/3! + 2.4⁴/4!) Any λ; allow one end error
3. [A1] 0.0959 (3 sf) SC unsupported answer 0.0959 scores B1 only not M1A1
4. [M1] 0.0959 > 0.05 Valid comparison Use of 0.9041 < 0.95 can recover either M1A1 or B1
5. [A1 FT] There is evidence that Jane's claim not justified or There is insufficient evidence to support Jane's claim OE. In context, not definite, e.g. not 'Jane is wrong', no contradictions. Condone omission of Jane.
6. [B1] Mean not constant so Poisson model not valid