Question 3 - A-Level Maths

Exam Board	Edexcel
Module	S3 (Statistics 3)
Year	2015
Session	June
Topic	Hypothesis test of a Poisson distribution

The number of accidents on a particular stretch of motorway was recorded each day for 200 consecutive days. The results are summarised in the following table.

Number of accidents	0	1	2	3	4	5
Frequency	47	57	46	35	9	6

Show that the mean number of accidents per day for these data is 1.6 A motorway supervisor believes that the number of accidents per day on this stretch of motorway can be modelled by a Poisson distribution. She uses the mean found in part (a) to calculate the expected frequencies for this model. Her results are given in the following table.
Number of accidents 0 1 2 3 4 5 or more
Frequency 40.38 64.61 \(r\) 27.57 11.03 \(s\)
Find the value of \(r\) and the value of \(s\), giving your answers to 2 decimal places.
Stating your hypotheses clearly, use a \(10 \%\) level of significance to test the motorway supervisor's belief. Show your working clearly.

Number of accidents	0	1	2	3	4	5 or more
Frequency	40.38	64.61	\(r\)	27.57	11.03	\(s\)