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Question 1 4 Marks
Visit the Australian Stock Exchange website, www.asx.com.au and from “Prices and research” drop-down menu, select “Company information”. Type in the ASX code “WPL” (Woodside Petroleum Limited), and find out details about the company. Also, type in the ASX code “WOR” (WorleyParsons Limited), and find out the details about that company. Both these companies trade in energy sector. Information available in the ASX website will be inadequate for your purpose, you will need to search the internet for more information. Your task will be to get the opening prices of WPL and WOR shares for every quarter from January 2003 to December 2015 (unadjusted prices). If you are retrieving the monthly prices, read the values in the beginning of every Quarter (January, April, July, October) for every year from 2003 to 2015. To provide you with some guidance as to what the unadjusted prices look like, two charts accompany this question obtained from ANZ Share Investing, Australia. After you have researched share prices and energy sector, answer the following questions:
(a) List all the quarterly opening price values in two tables, one for WPL and the other for WOR. Then construct a stem-and-leaf display with one stem value in the middle, and WPL leaves on the right side and WOR leaves on the left side. (Must use EXCEL or similar for the plot.) 1 mark
(b) Construct a relative frequency histogram for WPL and a frequency polygon for WOR on the same graph with equal class widths, the first class being “$0 to less than $10”. Use two different colours for WPL and WOR. Graph must be done in EXCEL or similar software. 1 mark
(c) For sector comparisons, draw a bar chart of market capital in 2015 (in Australian dollars) of the following companies in energy sector listed in ASX: WPL, WOR, ORG, STO, CTX and SOL. Graphing must be done in EXCEL or with similar software. 1 mark
(d) What proportion of stock prices (quarterly opening values) were above $40 for each of WPL and WOR? 1 mark
(Note: Use only the original values of share prices and not adjusted values.)
Question 2 4 Marks
The following table provides the prices of textbooks (in US dollars) randomly selected from five publishers from the website www.bookdepository.com. ISBN-13 of each book is provided along with the price. From the data answer the questions below for the publishers. (Website accessed on 10 Aug 2016.)
(a) Compute the mean, median, first quartile, and third quartile of prices for each publisher (with only the data provided in the table, do not add or change anything in the table) using the exact position, (n+1)f, where n is the number of observations and f the relevant fraction for the quartile. 1 mark
(b) Compute the standard deviation, range and coefficient of variation from the sample data of each publisher. 1 mark
(c) Draw a box and whisker plot for the prices of each publisher and put them side by side on one graph with the same scale so that the prices can be compared. (This graph must be done in EXCEL or similar software and cannot be hand-drawn.) 1mark
(d) Visit the www.bookdepository.com website and select a textbook ISBN-13 from the table above which has the same last digit as the last digit of your student ID and provide the full citation of that in Harvard citation style. 1 mark
Question 3 4 Marks
The Table below is taken from the Australian Bureau of Statistics website. It provides data on water use in Australian agricultural farms. (You can get the data from the URL: http://www.abs.gov.au/ausstats/abs@.nsf/0/A5A4DA2DF9F997A0CA2571AD007DDFD4?Opendocument. Totals provided may be higher since all possibilities may not be listed. The totals are not incorrect. MDB stands for Murray-Darling Basin and ML is megalitres).
Based on the information available in the table above -
(a) If a farm is randomly selected in Australia, what is the probability that it gets water from on-farm dams or tanks? 1 mark
(b) If a farm is randomly selected in Australia, what is the probability that it gets water from groundwater and is located in Queensland? 1 mark
(c) Given that a farm is located in the Murray-Darling basin (MDB, which spans parts of the states of NSW, VIC, ACT, QLD and SA), what is the probability that it takes water from rivers, creeks or lakes? 1 mark
(d) In New South Wales what proportion of farms do not take water from either irrigation channels or pipelines or river, creeks or lakes? 1 mark
Question 4 4 Marks
(a) The following data collected from the Australian Bureau of Meteorology Website (http://www.bom.gov.au/climate/data/?ref=ftr) gives the daily rainfall data (includes all forms of precipitation such as rain, drizzle, hail and snow) for the year 2015 in Hobart, Tasmania. The zero values indicate no rainfall and the left-most column gives the date. Assuming that the weekly rainfall event (number of days in a week with rainfall) follows a Poisson distribution (There are 52 weeks in a year and a week is assumed to start from Monday. The first week starts from 29 December 2014 – you are expected to visit the website and get the daily values which are not given in the table below. Make sure you put the correct station number. Ignore the last few days of 2015 if it exceeds 52 weeks.):
(i) What is the probability that on any given week in a year there would be no rainfall? 1 mark
(ii) What is the probability that there will be 3 or more days of rainfall in a week? 1 mark
(Question 4 continued next page)
(Question 4 continued)
(b) Assuming that the weekly total amount of rainfall (in mm) from the data provided in part (a) has a normal distribution, compute the mean and standard deviation of weekly totals.
(i) What is the probability that in a given week there will be between 6 mm and 12 mm of rainfall? 1 mark
(ii) What is the amount of rainfall if only 20% of the weeks have that amount of rainfall or higher? 1 mark
Question 5 4 Marks
The following data is taken from the UCI machine learning data repository (https://archive.ics.uci.edu/ml/datasets/Forest+Fires). It lists values of a few meteorological variables during forest fires. The table is only a part and the last 140 instances of the dataset – use only the values provided in the table and do not bring in additional instances from the website to answer the questions below.
(a) Test for normality of the variables Temperature, Relative humidity and Wind separately using normal probability plot. 2 marks
(b) Construct a 95% confidence interval for each of the variables in part (a). 1 mark
(c) Test the hypothesis that more areas in the forest burn when the temperature is above 250C than when it is below 250C. Use 1% level of significance. 1 mark
Instance No. Month Temperature (0C) Relative humidity (%) Wind (km/hr) Rain
(mm) Area burned (ha)
1 aug 21.9 42 2.2 0 174.63
2 mar 8.7 51 5.8 0 0
3 jan 5.2 100 0.9 0 0
4 jul 19.3 39 7.2 0 7.73
5 aug 16.2 63 2.7 0 16.33
6 aug 28.2 29 1.8 0 5.86
7 aug 20.5 58 2.7 0 42.87
8 aug 21.3 44 4.5 0 12.18
9 aug 20.9 50 2.2 0 16
10 sep 20.6 55 5.4 0 24.59
11 mar 11.6 48 5.4 0 0
12 aug 23.3 34 3.1 0 28.74
13 aug 23.3 34 3.1 0 0
14 feb 7.5 71 6.3 0 9.96
15 sep 20.7 46 2.7 0 30.18
16 sep 21.9 43 4 0 70.76
17 mar 15.2 19 7.6 0 0
18 feb 5.3 68 1.8 0 0
19 feb 10.1 62 1.8 0 51.78
20 sep 20.4 55 4.9 0 3.64
21 aug 24.3 33 3.6 0 3.63
22 aug 25.9 32 3.1 0 0
23 jun 28 34 4.5 0 0
24 jun 28 34 4.5 0 8.16
25 sep 22.8 46 4 0 4.95
26 aug 25 36 4 0 0
27 aug 21.3 41 3.6 0 0
28 sep 21.8 34 2.2 0 6.04
29 aug 27.9 27 2.2 0 0
30 sep 17 67 4.9 0 3.95
31 feb 14.2 46 4 0 0
32 sep 19.9 44 3.1 0 7.8
33 jul 23.4 31 5.4 0 0
34 feb 14.7 42 2.7 0 0
35 feb 8.2 53 9.4 0 4.62
36 jul 22.8 27 4.5 0 1.63
37 aug 26.4 33 3.6 0 0
38 aug 24.1 50 4 0 0
39 aug 27.5 27 4.9 0 746.28
40 jul 26.3 39 3.1 0 7.02
41 mar 13.8 24 5.8 0 0
42 aug 24.9 42 5.4 0 2.44
43 aug 24.8 36 4 0 3.05
44 aug 26.2 36 4.5 0 185.76
45 aug 30.8 19 4.5 0 0
46 jul 29.3 27 3.6 0 6.3
47 sep 22.3 48 4 0 0.72
48 aug 26.9 31 3.6 0 4.96
49 aug 20.4 56 2.2 0 0
50 aug 20.4 56 2.2 0 0
51 aug 27.9 33 2.2 0 2.35
52 aug 26.2 34 5.8 0 0
53 aug 24.6 44 4 0 3.2
54 sep 19.4 45 3.6 0 0
55 aug 23.3 40 4 0 6.36
56 aug 23.9 38 6.7 0 0
57 aug 20.9 66 4.9 0 15.34
58 aug 22.2 45 3.6 0 0
59 jul 23.8 51 1.8 0 0
60 aug 26.8 35 1.3 0 0.54
61 aug 14.2 73 2.7 0 0
62 aug 23.6 53 4 0 6.43
63 sep 19.1 46 2.2 0 0.33
64 sep 16.2 58 3.6 0 0
65 aug 25.5 29 1.8 0 1.23
66 apr 10.9 64 3.1 0 3.35
67 jul 14.8 78 8 0 0
68 sep 16.2 58 3.6 0 9.96
69 aug 17.3 80 4.5 0 0
70 aug 19.1 70 2.2 0 0
71 mar 8.9 35 8 0 0
72 sep 10.5 77 4 0 0
73 aug 19.3 61 4.9 0 0
74 aug 23.4 49 5.4 0 6.43
75 aug 11.8 88 4.9 0 9.71
76 aug 17.7 65 4 0 0
77 aug 17.4 54 3.1 0 0
78 aug 16.8 56 3.1 0 0
79 jul 17.9 48 2.7 0 0
80 aug 16.6 59 2.7 0 0
81 aug 19.9 50 4 0 82.75
82 aug 18.9 64 4.9 0 3.32
83 aug 15.5 72 8 0 1.94
84 aug 18.9 64 4.9 0 0
85 aug 18.9 64 4.9 0 0
86 sep 14.5 76 7.6 0 3.71
87 feb 4.6 82 6.3 0 5.39
88 feb 5.1 77 5.4 0 2.14
89 feb 4.6 59 0.9 0 6.84
90 mar 10.2 45 5.8 0 3.18
91 mar 11.2 41 5.4 0 5.55
92 mar 13.3 27 3.6 0 6.61
93 apr 13.7 33 9.4 0 61.13
94 apr 17.6 27 5.8 0 0
95 may 18 40 4 0 38.48
96 jun 14.3 79 4 0 1.94
97 jun 24.5 50 3.1 0 70.32
98 jun 26.4 35 2.7 0 10.08
99 jun 22.7 40 9.4 0 3.19
100 jul 27.2 28 1.3 0 1.76
101 jul 26.1 45 4 0 7.36
102 jul 18.2 82 4.5 0 2.21
103 jul 22.6 57 4.9 0 278.53
104 jul 30.2 25 4.5 0 2.75
105 jul 30.2 22 4.9 0 0
106 aug 23.4 40 5.8 0 1.29
107 aug 31 27 5.4 0 0
108 aug 33.1 25 4 0 26.43
109 aug 30.6 28 3.6 0 2.07
110 aug 24.1 43 6.3 0 2
111 aug 26.4 34 3.6 0 16.4
112 aug 19.4 71 7.6 0 46.7
113 aug 20.6 58 1.3 0 0
114 aug 28.7 33 4 0 0
115 aug 32.4 21 4.5 0 0
116 aug 32.4 27 2.2 0 0
117 aug 27.5 29 4.5 0 43.32
118 aug 30.8 30 4.9 0 8.59
119 aug 23.9 42 2.2 0 0
120 aug 32.6 26 3.1 0 2.77
121 aug 32.3 27 2.2 0 14.68
122 aug 33.3 26 2.7 0 40.54
123 aug 27.3 63 4.9 6.4 10.82
124 aug 21.6 65 4.9 0.8 0
125 aug 21.6 65 4.9 0.8 0
126 aug 20.7 69 4.9 0.4 0
127 aug 29.2 30 4.9 0 1.95
128 aug 28.9 29 4.9 0 49.59
129 aug 26.7 35 1.8 0 5.8
130 aug 18.5 73 8.5 0 0
131 aug 25.9 41 3.6 0 0
132 aug 25.9 41 3.6 0 0
133 aug 21.1 71 7.6 1.4 2.17
134 aug 18.2 62 5.4 0 0.43
135 aug 27.8 35 2.7 0 0
136 aug 27.8 32 2.7 0 6.44
137 aug 21.9 71 5.8 0 54.29
138 aug 21.2 70 6.7 0 11.16
139 aug 25.6 42 4 0 0
140 nov 11.8 31 4.5 0 0
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