Statistics assessment

The England andWales Rainfall (EWR) data set contains rainfall totals (measured in millimetres) that repre-
sent the average rainfall across England andWales for each season. The Central England Temperature (CET)
data set contains temperatures (measured in degrees Celsius) that represent the average temperature over an
area of central England for each season. The file temprain.txt contains the following five columns of data:
Year (year), TempJJA (summer CET), TempDJF (winter CET), RainJJA (summer EWR) and RainDJF (winter
EWR). Download this file from the module webpage http://vle.exeter.ac.uk/course/view.php?id=742
and write a short report with paragraphs that address each of the points listed below. Your report must
contain at most 500 words of text and at most six graphs. Do not include any R code in your report.
1. Describe and compare the distribution of the summer rainfall and the distribution of the winter rainfall,
using appropriate graphs and statistics.

2. (a) Discuss whether or not the distribution of the winter rainfall is well described by a Normal model,
using an appropriate graph.
(b) Suggest suitable values for the parameters of a Normal model for the winter rainfall. Calculate the
quartiles of this Normal model and compare these to the sample quartiles of the winter rainfall.
(c) Calculate the probability of the winter rainfall exceeding 400mm using your Normal model, and
comment briefly on whether or not this is likely to be a good estimate for the chance of this event
occurring.

3. (a) Describe the association between the temperature and rainfall in summer, and the association
between the temperature and rainfall in winter, using appropriate graphs and statistics.
(b) Use the data to estimate the chance of (i) a warm, dry summer in which the summer temperature
is greater than the median summer temperature and the summer rainfall is less than the median
summer rainfall; and (ii) a warm, wet summer in which the summer temperature is greater than
the median summer temperature and the summer rainfall is greater than the median summer
rainfall.

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