Question 1: Visit the Australian Stock Exchange website, www.asx.com.au and from "Prices and research" drop-down menu, select "Charting". Type in the ASX code "ORI" (Orica Limited), select OLHC Bar, and Timeframe "Monthly prices over 10 years". Click on "Create chart". After you create the chart, read the values in the beginning of every Quarter (January, April, July, October) for every year from 2001 to 2014. (ASX information may be incomplete and the values adjusted, not original, which will give you at most 60 percent marks. Read the note below if you wish to score higher marks.)
(a) List all the values in a table and then construct a stem-and-leaf display for the data.
(b) Construct a relative frequency histogram for these data with equal class intervals, the first class being "$0 to less than $5".
(c) Briefly describe what the histogram and the stem-and-leaf display tell you about the data. What effects would there be if the interval size is doubled, which means the first class will be "$0 to less than $10"?
(d) What proportion of stock prices were above $25?
(Note: To get more accurate values you will need to search the Internet - it is part of the assignment task to test your ability to find the correct information. If you use Etrade Australia, for example, as given in the figure below, use the opening price for the given quarter, which is the whisker to the left of each bar. For higher accuracy, use the interactive chart, and as you move the cursor in the interactive chart, the values will display in dollars and cents at the top.)
Question 2: From the data available at Australian Institute of Petroleum and Caltex, the standard unleaded petrol prices at the beginning of each year in metropolitan areas of different Australian states are given in the accompanying table.
(a) Compute the mean, median, first quartile, and third quartile for each state (with only the data provided for that state, do not fill missing values for any part of question 2) using the exact position, (n+1)f, where n is the number of observations and f the relevant fraction for the quartile.
(b) Compute the standard deviation, range and coefficient of variation from the sample data for each state.
(c) Draw a box and whisker plot for petrol prices of each state and put them side by side on the same scale so that the prices can be compared.
(d) Compare the box plots and comment on the skewness of the data.
Question 3: The Table below is taken from the Australian Bureau of Statistics website. It provides data on mental and behavioural problems of Australian residents. (You can get the data from Table 3 from the URL: https://www.abs.gov.au/AUSSTATS/[email protected]/DetailsPage/4364.0.55.0012011-12?OpenDocument. Star marks indicate possible errors, "np" means not published, and totals may be higher since all possibilities may not be listed. The totals are not incorrect.).
Based on the information available in the table above -
(a) What is the probability that a person, randomly selected, has mood (affected) problems and belongs to the age group 35 to 44?
(b) What is the probability that a person, randomly selected, belongs to the age group of 55 or over?
(c) Given that the person belongs to the age group of 45 to 54, what is the probability that he or she is suffering from alcohol and drug problems?
(d) Are different types of mental and behavioural problems independent of the gender?
Question 4: (a) The following data collected from the Australian Bureau of Meteorology Website (https://www.bom.gov.au/climate/data/?ref=ftr) gives the daily rainfall data for the year 2014 in Sydney (recorded in mm at Sydney Airport). The zero values indicate no rainfall and the left-most column gives the date. Assuming that Rainfall or No-Rainfall event follows a Poisson distribution:
(i) What is the probability that on any given week in a year there would be no rainfall?
(ii) What is the probability that there will be 2 or more days of rainfall in a week? (There are 52 weeks in a year and a week is assumed to start from Monday).
(b) Assuming that the weekly total amount of rainfall 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 4 mm and 12 mm of rainfall?
(ii) What is the amount of rainfall if only 8% of the weeks have that amount of rainfall or higher?
Question 5: According to Department of Infrastructure and Regional Development, Australian Government, the number of human fatalities in Australian roads for different states during the period 1985-2014 are given in the table below.
Table 5.1 Deaths by jurisdiction 1985 - 2014
Year NSW Vic Qld SA WA Tas NT ACT Australia
1985 1,067 683 502 268 243 78 67 33 2,941
1986 1,029 668 481 288 228 91 71 32 2,888
1987 959 705 442 256 213 77 84 36 2,772
1988 1,037 701 539 223 230 75 51 31 2,887
1989 959 776 428 222 242 80 61 32 2,800
1990 797 548 399 226 196 71 68 26 2,331
1991 663 503 395 184 207 77 67 17 2,113
1992 649 396 416 165 200 74 54 20 1,974
1993 581 435 396 218 209 58 44 12 1,953
1994 646 377 418 159 211 59 41 17 1,928
1995 620 418 456 181 209 57 61 15 2,017
1996 581 417 385 181 247 64 72 23 1,970
1997 576 377 360 148 197 32 60 17 1,767
1998 556 390 279 168 223 48 69 22 1,755
1999 577 383 314 151 218 53 49 19 1,764
2000 603 407 317 166 212 43 51 18 1,817
2001 524 444 324 153 165 61 50 16 1,737
2002 561 397 322 154 179 37 55 10 1,715
2003 539 330 310 157 180 41 53 11 1,621
2004 510 343 311 139 178 58 35 9 1,583
2005 508 346 330 148 163 51 55 26 1,627
2006 496 337 335 117 200 55 45 13 1,598
2007 435 332 360 124 235 45 58 14 1,603
2008 374 303 328 99 205 39 75 14 1,437
2009 454 290 331 119 191 63 31 12 1,491
2010 405 288 249 118 193 31 50 19 1,353
2011 364 287 269 103 179 24 45 6 1,277
2012 369 282 280 94 183 31 49 12 1,300
2013 333 243 271 98 162 36 37 7 1,187
2014 312 249 223 107 181 35 39 10 1,156
(a) Test for normality of the data for each state separately as well as for Australia as a whole.
(b) Through the construction of 95% confidence intervals, test if the mean annual rate of road fatality in Tasmania is significantly different from that of Northern Territory. State your assumptions.