9 JUNE 2005
Morning
1 hour 30 minutes
Additional materials:
Answer booklet
Graph paper
MEI Examination Formulae and Tables (MF2)
TIME 1 hour 30 minutes
- Write your name, centre number and candidate number in the spaces provided on the answer booklet.
- Answer all the questions.
- You are permitted to use a graphical calculator in this paper.
- The number of marks is given in brackets [ ] at the end of each question or part question.
- You are advised that an answer may receive no marks unless you show sufficient detail of the working to indicate that a correct method is being used.
- Final answers should be given to a degree of accuracy appropriate to the context.
- The total number of marks for this paper is 72.
1 A student is collecting data on traffic arriving at a motorway service station during weekday lunchtimes. The random variable \(X\) denotes the number of cars arriving in a randomly chosen period of ten seconds.
- State two assumptions necessary if a Poisson distribution is to provide a suitable model for the distribution of \(X\). Comment briefly on whether these assumptions are likely to be valid.
The student counts the number of arrivals, \(x\), in each of 100 ten-second periods. The data are shown in the table below.
Carry out a test at the \(5 \%\) level of significance to examine whether there is any association between type of customer and type of drink. State carefully your null and alternative hypotheses.