jam007
strengthFaculty of Engineering and Technology
Coursework Title: Statistical Report
Module Name: Applied Engineering Mathematics
Module Code: 5100BEUG
Level: 5
Credit Rating: 24
Weighting: 30%
Maximum mark available: 100%
Programmes: MEng / BEng Civil Engineering; MEng Architectural Engineering; MEng Building Services Engineering
Introduction
Your task is to write a report on a series of statistical tests, as described below.
Learning Outcome to be assessed
Apply statistical tests and investigate correlation
Detail of the task
Your task is to write a report on a series of statistical tests, as described below. Note that the data is ‘individual’ to each student, in that each student’s data depends on your 6 figure ID number. The variables a, b, c, d, e, and f are used, where abcdef is your ID number. If your ID were 184623, for example, then a = 1, b = 8, c = 4, d = 6, e = 2 and f = 3, so ‘af’ would represent 13 and ‘bcd’ would be 846.
You should test for significance at the 95% level throughout.
Note that the report should include an explanation of your calculations (a sample calculation, or a copy of an Excel spreadsheet showing the formulae, would be suitable). It should also include a discussion of your results from each section.
Your report is to address the following:
1. Investigate the probabilities of winning a lottery, based on a random choice of x balls from a set of y balls. You should consider the following values for x and y:
x |
y |
4 |
8 + af |
6 |
32.+ b |
5 |
36 + b |
7 |
24 + cd |
You should consider the two possible ways in which the balls can be handled once chosen. These two possibilities are:
a) Replace the ball after it has been chosen
b) Do not replace the ball after it has been chosen
(15 marks)
Mark detail: 3 marks for discussion, 1.5 marks for each answer to the 8 probabilities required)
2. Concentration levels of nitrogen dioxide in the air over a two month period are as shown in Appendix 1.
a) You are to produce a graph which shows the pollution levels with time, using the raw data. (4 marks)
b) Calculate the mean and standard deviation for the two month period
(2 marks)
c) You are to produce a graph which shows the variation in the pollution levels with time, using a five day moving average. (5 marks)
d) In no more than 100 words, compare the two graphs. (4 marks)
(total 15 marks)
3. A new bitumen additive is being tested. Results from tests on the stiffness modulus (measured in MPa) are as follows:
Old additive |
New additive |
2730 |
2418 |
2313 |
2711 |
2850 + bcd |
2176 |
2385 - fba |
2342 |
2540 |
2478 |
2763 |
2158 |
2882 |
2326 |
2821 |
1871 |
2544 |
2705 |
2543 + efb |
2936 |
2422 |
2281 |
2624 |
2770 |
2318 |
2633 |
2549 |
2337 |
1898 |
2730 |
2486 + 10 * dc |
2388 |
2790 + number of ‘1’s in the binary version of your ID number |
2012 – 10 * number of zeros in the binary version of your ID number |
2676 |
2259 |
2658 |
2045 |
2198 |
2075 |
a) Use the Mann-Whitney test to investigate whether there is a difference between the medians. (10 marks)
b) Use an appropriate statistical test to investigate whether there is a difference between the means of the stiffness moduli. (15 marks)
Note that 5 marks are for discussion of a) and b) (and you will be expected to compare the two). This leaves 8 marks for a) and 12 marks for b) for calculations, statements of the hypotheses and statement of the result.)
4. Consider the impact of faulty measuring equipment. How much difference would an incorrect reading make to your answers to question 3) (above)? You should consider 3 possible scenarios and calculate the statistical values for each of the three scenarios. You make the choice as to which values to change, and what high values to use:-
a) One zero value for one of the readings from the bitumen with the new additive.
b) One high value (up to 10 times the actual data value) for one of the readings from the bitumen with the new additive.
c) Three high values (up to 10 times the actual data value) for three of the readings from the bitumen with the old additive.
(18 marks)
Mark detail: 6 marks for each of a), b) and c).
Of each 6 marks, there are 4 marks for calculations, hypotheses and result, and 2 marks for discussion.
5. The data in the following table shows the approximate construction cost of a variety of bridges, together with the span length.
Span length (m) |
Approx. cost (£million) |
2500 |
380 |
7800 |
840 + fb |
126 |
22 |
41580 |
230 |
55000 |
1000 + ce |
36690 |
145 |
36000 |
1550 |
5128 |
380 + f + c |
6611 |
820 |
295 |
3 |
Consider the relationship between cost and bridge length. Calculate the correlation coefficient, produce a scatter diagram and calculate the equation of the line of best fit. (15 marks)
Mark detail: 11 marks for producing the scatter diagram together with the values for correlation coefficient and equation of line. 4 marks for discussion.
6. A survey has been carried out to investigate opinions on the various proposals for increasing London’s capacity for air travel. Respondents were asked to choose between three options, and were also asked to state their age range:
· A third runway at Heathrow Airport
· ‘Boris Island’ (a new airport in the Thames estuary)
· A second runway at Gatwick Airport
The responses were as follows
Age range (years) |
3rd runway at Heathrow |
‘Boris Island’ |
2nd runway at Gatwick |
< 30 |
90 + c |
120 |
30 |
30 – 45 |
50 |
59 - f |
e + 40 |
> 45 |
57 + 2e |
76 + d |
44 + number of 1s in binary version of your ID number |
You are to use the chi squared test to assess whether different age ranges responded differently to the questions.
(12 marks)
Mark detail: 9 marks for calculations, hypotheses and result, 3 marks for discussion.
What you should hand in
You should ensure that you state suitable hypotheses within your report whenever this is appropriate.
You must include sufficient information within your report to demonstrate that you have done your calculations correctly.
All graphs must have sensible titles, and clearly (and correctly) labelled axes.
Your report is to be submitted as ONE document through the Blackboard coursework submission facility. This document must be in either WORD or PDF.
Note that any assignment which is submitted differently will not be marked. You can copy and paste from Excel into Word easily.
Also note that you must wordprocess your document. Handwritten scanned pages are not acceptable.
Marking Scheme/Assessment Criteria
The marks for each section are shown within the task detail shown above.
Recommended reading
Lecture notes
Extenuating Circumstances
If something serious happens that means that you will not be able to complete this assignment, you need to contact the module leader as soon as possible. There are a number of things that can be done to help, such as extensions, waivers and alternative assessments, but we can only arrange this if you tell us. To ensure that the system is not abused, you will need to provide some evidence of the problem.
More guidance is available at https://www2.ljmu.ac.uk/student-administration/126427.htm
Any coursework submitted late without the prior agreement of the module leader will receive 0 marks.
Academic Misconduct
The University defines Academic Misconduct as ‘any case of deliberate, premeditated cheating, collusion, plagiarism or falsification of information, in an attempt to deceive and gain an unfair advantage in assessment’. This includes attempting to gain marks as part of a team without making a contribution. The Faculty takes Academic Misconduct very seriously and any suspected cases will be investigated through the University’s standard policy ( Academic Misconduct ). If you are found guilty, you may be expelled from the University with no award.
It is your responsibility to ensure that you understand what constitutes Academic Misconduct and to ensure that you do not break the rules. If you are unclear about what is required, please ask.
For more information you are directed to following the University web pages:
· Information regarding academic misconduct :
http://www2.ljmu.ac.uk/corporate/SPR/89510.htm
· Information on study skills : http://www2.ljmu.ac.uk/studysupport/
· Information regarding referencing :
https://www2.ljmu.ac.uk/studysupport/69049.htm
Appendix 1 Nitrogen Dioxide levels
Note that all values are in g/m3.
Date |
NO2 |
02/05/2015 |
55 |
03/05/2015 |
47 |
04/05/2015 |
78 |
05/05/2015 |
86 |
06/05/2015 |
69 |
07/05/2015 |
80 |
08/05/2015 |
90 |
09/05/2015 |
82 |
10/05/2015 |
54 |
11/05/2015 |
31 |
12/05/2015 |
61 |
13/05/2015 |
53-ab |
14/05/2015 |
68 |
15/05/2015 |
93 |
16/05/2015 |
85 |
17/05/2015 |
80 |
18/05/2015 |
75 |
19/05/2015 |
35 |
20/05/2015 |
54 |
21/05/2015 |
61 |
22/05/2015 |
52 |
23/05/2015 |
61+ed |
24/05/2015 |
31+fc |
25/05/2015 |
59 |
26/05/2015 |
26 |
27/05/2015 |
74 |
28/05/2015 |
68 |
29/05/2015 |
60 |
30/05/2015 |
71 |
31/05/2015 |
69 |
01/06/2015 |
87 |
02/06/2015 |
105 |
03/06/2015 |
52 |
04/06/2015 |
63 |
05/06/2015 |
51 |
06/06/2015 |
67 |
07/06/2015 |
102 |
08/06/2015 |
74 |
09/06/2015 |
43 |
10/06/2015 |
95-ca |
11/06/2015 |
64 |
12/06/2015 |
64 |
13/06/2015 |
64 |
14/06/2015 |
58 |
15/06/2015 |
74 |
16/06/2015 |
44 |
17/06/2015 |
58 |
18/06/2015 |
67 |
19/06/2015 |
48 |
20/06/2015 |
80 |
21/06/2015 |
62 |
22/06/2015 |
78 |
23/06/2015 |
31 |
24/06/2015 |
51 |
25/06/2015 |
29 |
26/06/2015 |
35 |
27/06/2015 |
19 |
28/06/2015 |
13 |
29/06/2015 |
58 |
30/06/2015 |
54 |
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