Assessment details for all students
Assessment item 2—Assignment 2
Due date: 6:00pm, Friday Week 10 ASSESSMENT
Weighting: 20% 2
Format: Submit one file online as .doc, .docx, .rtf or .pdf
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 100MB.
• 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. (In that case there is no need to write the equations.)
• 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. Also, no submission as an email attachment 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).
Plagiarism
CQU values academic honesty. Consequently, plagiarism will not be tolerated in assessment items. This assignment must be completed by each student individually.
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 “RMD” (ResMed Inc), and find out details about the company. Also, type in the ASX code “FPH” (Fisher and Paykel Healthcare), and find out the details about that company. Both these companies belong to healthcare 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 RMD and FPH shares for every quarter from January 2009 to December 2018 (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 2009 to 2018 (Total 40 observations). 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 financial sector, answer the following questions:
(a) List all the quarterly opening price values in two tables, one for RMD and the other for FPH. Then construct a stem-and-leaf display with one stem value in the middle, and RMD leaves on the right side and FPH leaves on the left side. (Must use EXCEL or similar for the plot.) 1 mark
(b) Construct a relative frequency histogram for RMD and a frequency polygon for FPH on the same graph with equal class widths, the first class being “$0 to less than $2”. Use two different colours for RMD and FPH. Graph must be done in EXCEL or similar software. 1 mark
(c) Draw a bar chart of market capitals (or total assets) in 2018 (in million Australian dollars) of 6 companies listed in ASX that trade in healthcare with at least AUD100 million in market capital. Graphing must be done in EXCEL or with similar software. 1 mark
(d) If one wishes to invest in RMD or FPH, what is the market recommendation (for example, from Morningstar, Fatprophets, InvestSmart, etc.)? If you cannot find the information, what would be your recommendation based on your research of these two companies (trend, P/E ratio, dividend yield, debt and Beta)? 1 mark
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(Note: Use only the original values of share prices and not adjusted values.)
Question 2 4 Marks
The table below lists the advertised weekly rents of one bedroom apartment with no carpark in Australian state capital CBDs (Sydney NSW 2000, Melbourne VIC 3000, Brisbane QLD 4000, Adelaide SA 5000, Perth WA 6000, and Hobart TAS 7000) in March 2019. The data are available in the website www.domain.com.au/rent. Consider the information as a random sample of different sizes.
Weekly rent of apartment (1 bed, 1 bath) in March 2019 in Australian state capitals.
Capital city Advertised rent per week (in AUD)
Sydney NSW 2000 530, 580, 1150, 825, 980, 450, 940, 610, 665, 690, 780, 800, 750, 715, 700, 680, 620, 590, 600, 570, 610, 625, 680, 690, 700
Melbourne VIC 3000 370, 620, 550, 515, 475, 460, 610, 290, 330, 350, 370, 380, 415, 520, 475, 490, 450, 420, 430, 375, 380
Brisbane QLD 4000 300, 330, 360, 390, 450, 490, 440, 190, 220, 317, 320, 365, 400, 410, 405
Adelaide SA 5000 325, 335, 295, 390, 450, 480, 360, 330, 350, 355
Perth WA 6000 320, 330, 340, 350, 280, 350, 350, 300, 300
Hobart TAS 7000 250, 280, 395, 360, 190, 400, 340
From the information provided in the table above,
(a) Compute the mean, median, first quartile, and third quartile of weekly rents for each city 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, mean absolute deviation and range for each city. 1 mark
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(c) Draw a box and whisker plot for the weekly rents of each city and put them side by side on one graph with the same scale so that the weekly rents for different cities can be compared. (This graph must be done in EXCEL or similar software and cannot be hand-drawn.) 1mark
(d) Write a paragraph on 1 bed, 1 bath apartment rents of each city, approximate number of such apartments available at the time you answer this question, and how does the rents compare if one chooses to rent one private room for one week through Airbnb (www.airbnb.com.au) for each of these locations. 1 mark
Question 3 4 Marks
The Table below is taken from the Australian Bureau of Statistics (ABS) website http://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/7111.02016-17?OpenDocument under Data Cubes in xls format in Table_1. It provides data on principal crops grown in Australia both in terms of land areas (hectares) and quantities (tonnes).
Based on the table above, answer the questions below assuming that production of other crops are negligible in comparison:
(a) If a tourist from overseas randomly picks a crop field to visit in Australia, what is the probability that he or she will end up in a canola field? 1 mark
(b) Given that a randomly chosen truck is carrying a crop that was grown in New South Wales (NSW), what is the probability that it is carrying wheat? 1 mark
(c) A factory gets barley from all states that grow it except Western Australia and Tasmania because of transportation costs. If a randomly selected truck delivers barley to the factory, what is the probability that the barley was grown in South Australia (SA)? Assume that the factory receives proportionate quantities as the yields of states. 1 mark
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(d) Visit the ABS website and determine which estimate of crop production in a given state was most unreliable. 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 and hail) for the year 2018 in Tully, Queensland (Station number 32042). 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.):
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(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
(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 50mm of rainfall? 1 mark
(ii) What is the amount of rainfall if only 12% of the weeks have that amount of rainfall or higher? 1 mark
Question 5 4 Marks
Download heart disease data (statlog/heart) from the UCI machine learning data repository (https://archive.ics.uci.edu/ml/machine-learning-databases/statlog/heart/). The dataset is about patients checked for heart disease. The value of 1 in the last column indicates absence and 2 indicates presence of heart disease. (Download both heart.dat and heart.doc files. The actual data is contained in heart.dat file. Open it with Excel, change text to columns with “Delimited” option followed by choosing “Space” as Delimiter.). From the data provided, answer the questions below:
(a) Test for normality of the following variables using normal probability plot (to be done in Excel or similar software):
Resting blood pressure (given in column 4 or D), Serum cholesterol (given in column 5 or E), Maximum heart rate achieved (given in column 8 or H) and Oldpeak (given in column 10 or J). 2 marks
(b) Construct a 90% confidence interval for each of the variables in part (a) assuming those are normally distributed separating the data between patients with heart disease and patients without heart disease. After all the confidence intervals have been constructed, identify any variable(s) that can be used to distinguish patients with heart disease from those who do not have heart disease (i.e., identify the variables where the confidence intervals do not overlap). 2 marks