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

\begin{itemize}
  \item Write your name, centre number and candidate number in the spaces provided on the answer booklet.
  \item Answer all the questions.
  \item You are permitted to use a graphical calculator in this paper.
\end{itemize}

\begin{itemize}
  \item The number of marks is given in brackets [ ] at the end of each question or part question.
  \item 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.
  \item Final answers should be given to a degree of accuracy appropriate to the context.
  \item The total number of marks for this paper is 72.
\end{itemize}

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.\\
(i) 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.

\hfill \mbox{\textit{OCR MEI S2 2005 Q9}}