Reference no: EM13922598

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.