Edexcel FS1 2019 June — Question 5

Exam BoardEdexcel
ModuleFS1 (Further Statistics 1)
Year2019
SessionJune
TopicHypothesis test of a Poisson distribution

  1. Information was collected about accidents on the Seapron bypass. It was found that the number of accidents per month could be modelled by a Poisson distribution with mean 2.5 Following some work on the bypass, the numbers of accidents during a series of 3-month periods were recorded. The data were used to test whether or not there was a change in the mean number of accidents per month.
    1. Stating your hypotheses clearly and using a \(5 \%\) level of significance, find the critical region for this test. You should state the probability in each tail.
    2. State P(Type I error) using this test.
    Data from the series of 3-month periods are recorded for 2 years.
  2. Find the probability that at least 2 of these 3-month periods give a significant result. Given that the number of accidents per month on the bypass, after the work is completed, is actually 2.1 per month,
  3. find P (Type II error) for the test in part (a)