Question 1 4 Marks Visit the Australian Stock Exchange website, www.asx.com.au and from â€śPrices and researchâ€ť drop-down menu, select â€śCompany informationâ€ť. Type in the ASX code â€śSYDâ€ť (Sydney Airport), and find out details about the company. Also, type in the ASX code â€śALXâ€ť (Atlas Arteria), and find out the details about that company. Both these companies belong to industrials sector and within the industry group transportation. 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 SYD and ALX 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. After you have researched share prices and industrials sector (transportation group), answer the following questions: (a) List all the quarterly opening price values in two tables, one for SYD and the other for ALX. Then construct a stem-and-leaf display with one stem value in the middle, and SYD leaves on the right side and ALX leaves on the left side. (Must use EXCEL or similar for the plot.) 1 mark (b) Construct a relative frequency histogram for SYD and a frequency polygon for ALX on the same graph with equal class widths, the first class being â€ś$0 to less than $2â€ť. Use two different colours for SYD and ALX. 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 industrials (transportation) 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 SYD or ALX, 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 (Question 1 continued next page) (Question 1 continued) (Note: Use only the original values of share prices and not adjusted values.) Question 2 4 Marks The table below lists the prices of some common household white goods in Australia. Consider the information as data from simple random sampling of different sample sizes. Prices of white goods in Australian stores. Description Advertised or listed price (in AUD) 50â€ť 4K smart TV 439.99, 499.99, 880.00, 888.00, 499.00, 895.00, 595.00, 429.00, 699.00, 519.99, 1495.00, 454.00, 629.00, 602.00, 481.95, 498.00, 434.00, 752.00, 599.00, 469.95, 799.00, 480.15, 695.99, 929.33, 1395.00, 1295.00 300L frost-free Fridge 699, 449, 678, 849, 1199, 787, 694, 698, 878, 489, 595, 538, 999, 649, 1009 30L Microwave oven 180, 119, 129, 99, 139, 249, 333, 200, 168, 185, 170, 233, 165, 215, 176, 246, 280, 140, 259, 288, 348, 268, 349, 242 7kg top load clothes Washer 589, 445, 598, 744, 824, 699, 579, 649, 449, 769, 599, 597, 628 5kg vented clothes Dryer 399, 395, 495, 398, 395, 448, 418, 346, 478 From the information provided in the table above, (a) Compute the mean, median, first quartile, and third quartile of weekly rents for each of the white goods 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 of the white goods. 1 mark (Question 2 continues on to next page) (Question 2 continued) (c) Draw a box and whisker plot for the prices of each of the white goods and put them side by side on one graph with the same scale so that the prices for different white goods can be compared. (This graph must be done in EXCEL or similar software and cannot be hand-drawn.) 1mark (d) Write a paragraph on annual running cost and energy use per year in Australia for each of these white goods. Provide URLs from which you extracted the information and the dates on which you visited the Websites. 1 mark Question 3 4 Marks The Table below is taken from the Australian Bureau of Statistics (ABS) website https://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/5501.0.55.0012014-15 Final?OpenDocument Data Cubes Table 1 â€“ Government Financial Estimates, Australia (Table 3 inside spreadsheet). It provides data on revenue of different states in Australia as well as expenses (in million dollars). Based on the table above on the distribution of revenues, answer parts (a), (b) and (c) of the questions below: (a) What proportion of total income for all states and territories in Australia is coming from taxation? 1 mark (b) If Queensland government randomly picks $1 million from an income stream to be spent for an environmental cause, what is the probability that it is coming from Interest income? 1 mark (c) Given that the Federal government has some surplus money to be given as Capital grant to a state at random for rail expansion, what is the probability that the money will go to Tasmania? 1 mark (d) Visit the ABS website and determine which states are in the best and worst positions as to GFS Net Operating Balance. 1 mark Question 4 4 Marks 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 Innisfail, Queensland (Station number 32025). The zero values indicate no rainfall and the left-most column gives the date. (a) 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.): (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 4 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 20mm and 60mm 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 Download Spambase Data Set from the UCI machine learning data repository (https://archive.ics.uci.edu/ml/datasets/Spambase). The dataset is about identifying emails as being spam or non-spam. The value of 1 in the last column indicates spam and 0 indicates non-spam for a given email (Each row captures the characteristics of one email and the sample size of number of emails is 4601.). (Download both spambase.dat and spambase.names files. The actual data is contained in spambase.dat file. Open it with Excel, change text to columns with â€śDelimitedâ€ť option followed by choosing â€śCommaâ€ť as Delimiter.). The name of the attribute (column title) will come from spambase.names file; for example, 1st column is â€śmakeâ€ť, 2nd column is â€śaddressâ€ť, 3rd column is â€śallâ€ť, etc. The values in the table indicate the number of times (frequency) of these words occurring in a given email. From the data provided, answer the questions below: (a) Test for normality of the variables where more than 50% of the values are non-zeros using normal probability plot (to be done in Excel or similar software. COUNTIF function in Excel can be used to find the number of zeros in any column): 2 marks (b) Construct a 90% confidence interval for each of the variables checked for normality in part (a) assuming those are normally distributed separating the data between spam and non-spam emails. After all the confidence intervals have been constructed, identify any variable(s) that can be used to distinguish between spam and non-spam emails (i.e., identify the variables where the confidence intervals do not overlap). 2 marks