### Recent Question/Assignment

Assessment details for all students
Due: 19 May 2017
Assessment criteria
• This assignment must be typed, word-processed or clearly hand-written (but plots and graphs must be done using EXCEL or equivalent software), and submitted online as a single file through Moodle. Important note: The file size must not be over 50MB.
• Microsoft Excel allows students to cut and paste information easily into Microsoft Word documents. Word also allows the use of Microsoft Equation Editor to produce all necessary formulae (use of these are recommended).
• It is expected that Excel would be used to assist in statistical calculations for questions in this assignment. Where Excel is used, use copy function, “Snipping tool” or similar to cut and paste relevant parts of the spreadsheet to verify that you have done the work.
• For those questions where Excel is not used to do the computations, all formulae and working must be included to obtain full marks.
• Only one file will be accepted in any of the formats mentioned above. No zipped file or any other file extension will be accepted.
• There will be late submission penalty for submissions beyond the deadline unless prior approval is obtained from the Unit Coordinator through the extension system in Moodle. Under no circumstances any submission that is late beyond 14 days from the deadline of Friday of Week 10 will be marked, or get any score other than zero.
Assignment markers will be looking for answers which
• demonstrate the student’s ability to interpret and apply the statistical techniques in the scenarios and
• use statistical techniques as decision making tools in the business environment.
Full marks will not be awarded to answers which simply demonstrate statistical procedures without comment, interpretation or discussion (as directed in the questions).
Question 1 4 Marks
(a) List all the quarterly opening price values in two tables, one for COH and the other for RHC. Then construct a stem-and-leaf display with one stem value in the middle, and COH leaves on the right side and RHC leaves on the left side. (Must use EXCEL or similar for the plot.) 1 mark
(b) Construct a relative frequency histogram for COH and a frequency polygon for RHC on the same graph with equal class widths, the first class being “\$0 to less than \$10”. Use two different colours for COH and RHC. Graph must be done in EXCEL or similar software. 1 mark
(c) For sector comparisons, draw a bar chart of annual dividends in 2016 (in Australian cents) of the following companies in healthcare sector listed in ASX: COH, RHC, SHL, RMD, SRX, ANN and CSL. Graphing must be done in EXCEL or with similar software. 1 mark
(d) What proportion of stock prices (quarterly opening values) were above \$60 for each of COH and RHC? 1 mark

(Note: Use only the original values of share prices and not adjusted values.)
Question 2 4 Marks
There are four major supermarkets and grocery chains in Australia, which are Woolworths Ltd with a market share of 33.6% and brand names Woolworths, Safeway and Thomas Dux; Wesfarmers Ltd with a market share of 29.3% and brand names Coles and Bi-Lo; ALDI Stores Supermarket Pty Ltd with a market share of 8.9% and brand name ALDI; and Metcash Ltd with a market share of 7.1% and brand names IGA and Foodland. Details about these companies can be found in the Website http://clients1.ibisworld.com.au/reports/au/industry/majorcompanies.aspx?entid=1834. The following table provides the percent changes in sales revenue for each of these companies from the previous financial year. From the data answer the questions below for the supermarkets. (Website accessed on 22 February 2017.)
Annual percentage change in sales revenue
Year Woolworths Wesfarmers ALDI Metcash
2007-08 9.29 12.90
2008-09 4.48 -3.00 3.35
2009-10 3.45 -8.50 5.50 8.73
2010-11 6.82 5.84 7.00 4.77
2011-12 0.83 5.83 9.00 7.07
2012-13 6.10 5.30 19.00 2.20
2013-14 3.00 4.30 12.00 -1.10
2014-15 3.30 5.60 14.30 0.70
2015-16 -0.30 6.00 25.00 0.30
(a) Compute the mean, median, first quartile, and third quartile of revenue changes for each supermarket (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 data in the table for each supermarket. 1 mark
(c) Draw a box and whisker plot for the percent changes of each supermarket and put them side by side on one graph with the same scale so that the percent changes can be compared. (This graph must be done in EXCEL or similar software and cannot be hand-drawn.) 1mark
(d) Visit the IBISworld website and identify at least three other supermarket and grocery chains in Australia and quote the market share of each. 1 mark
Question 3 4 Marks
The Table below is taken from the Australian Government’s Department of Health. It provides data on mental health workforce distribution in Australia by States and Profession. The data is taken from the website http://www.health.gov.au/internet/publications/publishing.nsf/Content/mental-pubs-m-mhsrraev-toc~mental-pubs-m-mhsrraev-8~mental-pubs-m-mhsrraev-8-3#st1. In the table FTE stands for full-time equivalent, MHN for mental health nurse, OT for occupational therapist, MHW for mental health worker and HW for health worker.

Based on the information available in the table above and the fact that total number of mental health workers in WA, VIC, TAS, QLD, SA, NT and NSW were at the time 28 000, 66 000, 7 500, 51 000, 21 000, 2 000 and 76 000, respectively, answer the questions below:
(a) If a mental health worker is randomly selected in Australia, what is the probability that she or he is a social worker? 1 mark
(b) If a mental health worker is randomly selected in Australia, what is the probability that she or he is a clinical psychologist and located in Tasmania? 1 mark
(c) Given that the mental health worker is located in South Australia, what is the probability that she or he is an occupational therapist? 1 mark
(d) What percentage of psychologists live in either New South Wales or Victoria? 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 2016 in Perth, Western Australia. 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 4 January 2016 – you are expected to visit the website and get the daily values which are not given in the table below. Part of the 52nd week runs into 2017.):
(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 2 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 10mm and 20mm of rainfall? 1 mark
(ii) What is the amount of rainfall if only 15% 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/Bike+Sharing+Dataset). It lists the number of bikes rented (Count) as recorded by Capital Bikeshare System, Washington D.C. and the weather conditions (1 = clear or partly cloudy, 2 = misty, 3 = light snow or light rain, and 4 = heavy rain and/or thunderstorm). The table is a subset of 200 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, Humidity and Windspeed 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 less bikes are rented when the weather condition is 3 or 4 compared to the weather condition 1 or 2. Use 1% level of significance. 1 mark
Weather Temperature (0C) Humidity (%) Windspeed (km/hr) Count
2 14.1 80.6 10.7 985
2 14.9 69.6 16.7 801
1 8.1 43.7 16.6 1349
1 8.2 59.0 10.7 1562
1 9.3 43.7 12.5 1600
1 8.4 51.8 6.0 1606
2 8.1 49.9 11.3 1510
2 6.8 53.6 17.9 959
1 5.7 43.4 24.3 822
1 6.2 48.3 15.0 1321
2 6.9 68.6 8.2 1263
1 7.1 60.0 20.4 1162
1 6.8 47.0 20.2 1406
1 6.6 53.8 8.5 1421
2 9.6 49.9 10.6 1248
1 9.5 48.4 12.6 1204
2 7.2 53.8 13.0 1000
2 8.9 86.2 9.8 683
2 12.0 74.2 14.0 1650
2 10.7 53.8 13.1 1927
1 7.3 45.7 23.7 1543
1 2.4 40.0 11.5 981
1 4.0 43.7 16.5 986
1 4.0 49.2 10.6 1416
2 9.2 61.7 8.7 1985
3 8.9 86.3 19.7 506
1 8.0 68.8 7.6 431
2 8.3 79.3 8.3 1167
1 10.7 55.1 22.9 1872
1 12.0 42.1 8.1 2133
2 12.1 77.5 14.8 1891
3 16.0 0.0 17.5 623
1 13.5 59.5 14.8 2132
1 15.8 52.7 18.1 2417
1 13.3 49.7 9.2 2046
2 13.0 65.6 12.3 2056
3 11.0 91.8 14.6 1685
2 12.3 68.6 17.3 2227
2 12.9 65.4 13.2 2252
2 16.9 81.9 16.8 2162
1 19.2 54.0 7.4 3267
1 18.3 67.1 15.2 3126
3 17.7 88.8 22.8 795
1 18.7 48.0 20.3 3744
1 21.0 54.3 11.0 3429
2 20.7 66.6 10.6 3204
1 24.4 61.4 16.2 3944
1 18.8 40.7 21.8 4189
2 13.8 73.0 14.7 1683
2 31.3 67.7 13.9 3974
1 29.3 30.5 19.6 4968
1 25.4 35.4 17.0 5312
1 26.0 45.6 8.3 5342
2 26.6 65.3 9.3 4906
1 27.8 60.0 8.2 4548
1 29.0 59.8 12.6 4833
1 31.8 62.2 9.2 4401
2 33.1 56.8 10.0 3915
2 25.8 68.8 13.8 3767
1 26.6 73.6 9.6 4844
1 28.6 67.0 8.0 5119
2 28.7 66.7 6.8 4744
2 26.0 74.6 10.4 4010
2 27.9 77.0 11.5 4835
1 30.1 70.8 11.5 4507
2 29.9 70.3 16.0 4790
1 29.7 57.3 14.9 4991
1 29.0 56.2 20.4 4334
1 26.1 55.5 10.7 4634
1 26.2 54.8 8.4 5204
1 26.9 59.8 5.6 5058
1 26.9 63.9 9.5 5115
2 26.4 72.7 9.4 4727
1 27.4 71.7 12.4 4484
1 29.1 74.2 13.8 4940
2 27.6 79.0 14.3 3351
3 22.1 88.7 23.0 2710
3 24.6 91.7 6.5 1996
3 26.0 94.0 12.9 1842
2 26.7 89.8 8.3 3544
1 27.1 75.4 10.3 5345
1 26.8 71.4 7.7 5046
1 26.4 69.2 6.0 4713
1 26.7 71.3 9.5 4763
1 27.6 69.7 11.2 4785
1 20.9 68.4 1.5 4985
1 21.4 70.1 3.0 5409
1 22.2 72.8 4.3 5511
1 23.4 73.4 2.8 5117
2 23.2 80.9 9.6 4563
3 22.3 90.6 16.6 2416
2 24.2 89.7 9.5 2913
2 22.6 71.6 15.0 3644
1 20.8 48.3 17.3 5217
1 21.0 48.7 18.9 5041
1 21.9 58.0 11.8 4570
2 21.8 70.2 7.4 4748
3 22.2 89.5 16.3 2424
3 10.4 88.3 23.5 627
1 13.1 62.4 11.8 3331
1 13.9 70.3 7.1 3669
1 16.4 68.4 9.1 4068
1 15.5 71.9 5.5 4186
3 18.7 93.0 9.2 1817
2 14.0 57.6 20.5 3053
1 11.2 41.0 11.3 3392
1 13.5 50.2 15.0 3663
2 19.0 68.5 12.5 3520
3 18.3 91.0 9.2 2765
3 17.1 96.3 8.0 1607
3 19.0 95.0 15.6 2594
3 16.8 97.0 17.8 705
1 10.9 58.0 16.1 3322
1 11.9 69.6 5.5 3620
1 11.3 50.8 15.6 3190
2 10.8 78.0 8.2 2832
2 10.9 68.8 11.8 2947
1 11.6 62.2 10.3 3784
1 14.5 49.6 9.9 4375
2 10.5 72.3 9.0 2802
1 10.9 56.2 13.0 3830
2 11.5 54.0 7.8 3831
3 9.2 73.1 19.4 2169
1 5.2 46.5 27.4 1529
1 9.1 41.1 11.2 3422
2 13.1 50.9 9.5 3922
1 14.3 53.1 12.2 4169
2 13.0 75.3 6.1 3005
1 11.8 35.0 15.1 4118
1 14.8 47.7 14.9 4911
1 19.1 48.9 13.9 5298
1 23.2 61.8 15.9 5847
1 23.5 50.7 7.7 6312
1 22.9 58.0 10.0 6192
2 17.9 84.2 7.6 4378
2 21.1 75.6 7.4 7836
2 19.4 81.0 8.5 5892
1 22.3 72.9 10.9 6153
1 23.0 80.8 8.1 6093
2 21.8 82.1 6.0 6230
1 22.7 83.1 7.9 6871
2 24.7 69.4 7.8 8362
2 20.6 88.5 12.9 3372
2 17.9 88.1 14.8 4996
1 18.3 47.8 25.9 5558
1 13.3 29.0 12.5 5102
1 19.9 48.1 19.5 5698
1 20.3 43.9 21.4 6133
2 15.2 58.1 9.3 5459
2 17.4 73.8 16.8 6235
2 17.5 67.6 11.5 6041
1 17.8 50.4 20.9 5936
1 23.4 68.3 19.0 6624
3 16.3 83.5 23.1 1027
2 13.2 76.7 20.3 3214
1 16.9 45.4 16.7 5633
1 19.5 42.8 8.0 6196
2 20.4 75.7 11.8 5026
1 18.8 40.1 23.3 6233
2 15.4 49.0 8.7 4220
1 33.6 50.6 7.7 6786
1 32.5 57.7 9.2 5713
1 31.6 60.0 11.1 6591
2 27.3 84.4 14.0 5870
3 24.4 86.5 14.3 4459
2 27.4 76.3 6.3 7410
1 30.4 69.4 9.3 6966
1 30.8 65.5 14.2 7592
1 31.0 61.3 10.5 6685
1 29.6 62.4 11.4 6597
1 30.0 66.9 10.3 7105
1 29.2 70.4 11.1 7216
1 29.4 67.8 9.5 7580
1 30.9 66.0 8.7 7261
2 31.4 64.3 14.5 7175
1 32.5 61.3 17.2 6824
1 31.5 65.3 19.5 5464
2 30.9 65.4 8.7 7013
2 30.2 70.4 7.8 7273
2 30.8 67.3 7.4 7534
1 21.6 58.3 9.0 6889
2 21.4 64.9 6.1 6778
3 24.2 87.2 7.0 4639
2 27.0 79.4 4.5 7572
2 27.0 72.3 7.9 7328
2 19.6 69.5 26.7 4459
3 18.0 88.0 24.0 22
2 13.0 82.5 14.3 1096
2 14.7 66.7 11.2 5566
2 15.0 58.2 10.5 5986
1 14.6 52.2 17.8 5847
2 14.1 49.1 18.1 5138
1 13.4 53.3 12.0 5107
1 13.1 49.4 15.8 5259
2 13.4 55.7 25.1 3623
1 10.9 44.1 27.3 1749
1 10.1 51.5 8.9 1787
2 9.5 79.1 5.2 920
2 11.9 73.5 11.3 1013
3 10.0 82.3 21.2 441