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MATH20811 Practical Statistics : Coursework 2
The marks awarded for this coursework constitute 30% of the total assessment
for the module. It is envisaged that it will take the average student
about 15 hours to complete.
The submission deadline is 10.00 am on Monday 2 December
2019.
Late Submission of Work: Any student’s work that is submitted after
the given deadline will be classed as late, unless an extension has already
been agreed via mitigating circumstances or a DASS extension. The following
rules for the application of penalties for late submission are quoted from
the University guidance on late submission document, version 1.3 (dated
July 2019).
”Any work submitted at any time within the first 24 hours following the
published submission deadline will receive a penalty of 10% of the maximum
amount of marks available. Any work submitted at any time between 24
hours and up to 48 hours late will receive a deduction of 20% of the marks
available, and so on, at the rate of an additional 10% of available marks deducted
per 24 hours, until the assignment is submitted or no marks remain.”
Your submitted solutions should all be in one document and be prepared
using LaTex.
For each of the questions you should provide explanations as to how
you completed what is required, show your working and also comment on
computational results, where applicable.
When you include a plot be sure to give it a title and label the axes
correctly.
When you have written or used R code to answer any of the parts, then
you should list this R code after the particular written answer to which it
applies. This may be the R code for a function you have written and/or
code you have used to produce numerical results and plots.
Using LaTex, you can include R code and output from R using the
verbatim environment. ie. type
\begin{verbatim}
copy and paste lines of text from R here
\end{verbatim}
Your file should be submitted through the module site on Blackboard
to the Turnitin assessment entitled ”MATH20811 CW2” by the above time
and date. The work will be marked anonymously on Blackboard so please
ensure that your filename is clear but that it does not contain your name
and student id number. Similarly, do not include your name and id number
in the document itself.
Turnitin will generate a similarity report for your submitted document
and indicate matches to other sources, including billions of internet documents
(both live and archived), a subscription repository of periodicals, journals
and publications, as well as submissions from other students . Please
ensure that the document you upload represents your own work and is written
in your own words. The Turnitin report will be available for you to see
shortly after the due date.
This coursework should hopefully help to reinforce some of the methodology
you have been studying, as well as the skills in R you have been
developing in the module so far.
1. The following table gives the numbers of road casualties in Greater
London during 2013, categorised as being either ”fatal”, ”serious” or
”slight” and grouped by five modes of transport.
Casualty Severity
Fatal Serious Slight Sum
Mode of Transport Pedestrian 65 773 4343 5181
Pedal Cycle 14 475 4134 4623
Powered 2 Wheeler 22 488 3992 4502
Car 25 310 9850 10185
Other Vehicles 6 146 2556 2708
Sum 132 2192 24875 27199
The question of interest is whether the five modes of transport differ in
their respective probabilities of different casualty severity. You should
regard the row sums as being fixed quantities here.
(i) Given the description of the data, write down a suitable probability
model for this matrix of counts.
[2 marks]
(ii) Read the data as a matrix into R and label the two dimensions
appropriately.
Calculate appropriate proportions and comment informally on
the question of interest given above.
[5 marks]
(iii) Present the proportions data graphically and comment on the
resulting plot.
[5 marks]
(iv) State the relevant statistical hypotheses and test them using a
significance level α = 0.05 and a critical value from the asymptotic
null distribution of your test statistic. (You should clearly
state what this distribution is.) State your conclusions.
[3 marks]
(v) Print out appropriate sets of residuals and comment on their
values in the light of the conclusions you made in part (iv).
[3 marks]
(vi) Write your own code in R to obtain B = 5000 values of the test
statistic, each one calculated using a set of data simulated under
the assumption that the null hypothesis is true. You should aim
to efficiently make use of for loops in doing this.
Produce a histogram of these simulated values, superimpose the
plot of the asymptotic null distribution and comment informally
on the goodness-of-fit.
[6 marks]
(vii) Construct approximate 95% confidence intervals for (a) the difference
between the probability that a pedestrian is seriously injured
and the probability that a car driver is seriously injured
and (b) for cyclists only, the difference between the probabilities
of a serious injury and a slight injury.
[6 marks]
[Total marks = 30]

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