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Assignment for MTMG37\\\vspace{5mm}
Data analysis for weather and climate research\\
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The England and Wales Precipitation (EWP) dataset is a single time
series of rainfall amounts constructed from about 60 rain gauges.  The
file \verb|ewp.txt| (available from the module web page) contains the
seasonal and annual rainfall totals (in millimetres) for the years
1767 to 2001.  The four seasons are winter (December, January,
February), spring (March, April, May), summer (June, July, August) and
autumn (September, October, November).

The assignment is to perform a statistical analysis of the EWP data
and to summarise your analysis in a written report.  The assignment
will be assessed based on your report, which should address in
separate sections each of the five points listed below, and should not
exceed 10 pages (including figures).

The assignment represents 100\% of the marks for this course and your
work should be done individually.  Marks will be awarded for
appropriate choices of method, correct implementation, and quality of
interpretation and presentation.  The report must be submitted to
the Department Office before 5pm on Thursday 8 April 2004.\\

\noindent P.T.O.

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\begin{enumerate}
\item Summarise the main features of the data and compare the rainfall
      in the four seasons.  [5~marks]
\item If total annual rainfall is less than 700mm then drought
      measures need to be taken.  How often, on average, has this
      situation arisen?  Drought measures are to be imposed in summer
      depending on the total rainfall in December to May.  Estimate an
      amount of rainfall such that if the total rainfall in December
      to May falls below this amount then the probability that annual
      total rainfall will be less than 700mm is 0.5.  [5~marks]
\item A colleague used a Normal distribution as a probability model
      for total autumn rainfall and used the model to estimate the
      probability of exceeding the amount recorded in autumn 2000.
      Fit this model and estimate the probability.  Now estimate the
      probability using a Gamma distribution.  (Note that in MINITAB
      the `first shape parameter' is the parameter $\alpha$ in the
      lecture notes and the `second shape parameter' is $1/\beta$.)
      Comment on the reliability of these two probability estimates.
      [10~marks]
\item Assess the evidence for the hypothesis that winter and summer
      rainfall totals have equal population means.  Provide point
      and interval estimates for the difference in means.  [10~marks]
\item Describe and assess the strength of evidence for time trends in
      rainfall in each of the four seasons.  [20~marks]
\end{enumerate}

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