3 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 .

1. Assume that the number of accidents per year follows a Poisson distribution.
   1. State null and alternative hypotheses for a test of Jane's claim.
   2. Test at the \(5 \%\) significance level whether Jane's claim is justified.
2. Jane finds that the number of accidents per year has been gradually increasing over recent years. State how this might affect the validity of the test carried out in part (a)(ii).