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 “CCL” (Coca-Cola Amatil Limited), and find out details about the company. Your task will be to get the opening prices of a CCL share for every quarter from January 2001 to December 2015. If you are working with the monthly prices, read the values in the beginning of every Quarter (January, April, July, October) for every year from 2001 to 2015. It is part of the assignment task to test your ability to find the information from an appropriate website. If you are unable to do so, you may read the values from the chart provided below obtained from Etrade Australia. Obviously, reading from the chart will not be accurate and you may expect around 60 percent marks with such inaccuracy. After you have recorded the share prices, answer the following questions:
(a)    List all the values in a table and then construct a stem-and-leaf display for the data.    1 mark
(b)    Construct a relative frequency histogram for these data with equal class widths, the first class being “$4 to less than $6”.                                 1 mark
(c)    Briefly describe what the histogram and the stem-and-leaf display tell you about the data. What effects would there be if the class width is doubled, which means the first class will be “$4 to less than $8”?                                    1 mark
(d)    What proportion of stock prices were above $10?                    1 mark

Question 2    4 Marks
The following table provides the median weekly rents of a 3-bedroom house of a few randomly selected suburbs in four capital cities of Australia – Sydney, Melbourne, Brisbane and Perth – for March 2016. The data is obtained from the website https://www.realestate.com.au/neighbourhoods/. From the data answer the questions below for the capital cities.

(a)    Compute the mean, median, first quartile, and third quartile for each capital city (with only the data provided for that city, do not add/delete values for any new/given suburb 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.    1 mark
(b)    Compute the standard deviation, range and coefficient of variation from the sample data for each city.    1 mark
(c)    Draw a box and whisker plot for the median weekly rents of each city and put them side by side on the same scale so that the prices can be compared.       1mark
(d)    Compare the box plots and comment on the distribution of the data.       1 mark

Question 3    4 Marks
The Table below is taken from the Australian Bureau of Statistics website. It provides data on energy use of households – almost all houses use mains electricity but some use additional energy sources such as gas and solar. (You can get the data from Table 1 from the URL: http://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/4602.0.55.001Mar%202014?OpenDocument.) Missing cells indicate data 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 an Australian household, randomly selected, uses solar as a source of energy?                                    1 mark
(b)    What is the probability that an Australian household, randomly selected, uses mains gas and is located in Victoria?                                    1 mark
(c)    Given that a household uses LPG/bottled gas, what is the probability that the household is located in South Australia?                                        1 mark
(d)    Is the percentage of Australian households using mains gas independent of the state?    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 for the year 2015 in Brisbane. 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 29 December 2014 – you are expected to visit the website and get the daily values which are not given in the table below. Make sure you put the correct station number. Ignore the last few days of 2015 if it exceeds 52 weeks.):
(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 5 mm and 10 mm of rainfall?     1 mark
(ii) What is the amount of rainfall if only 13% 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/Wine+Quality). It lists a few attributes of red wine, randomly sampled from thousands of bottles, which can be classified as of good, medium and poor quality.
(a) Test for normality of all the variables separately for good wine using normal probability plot.           2 marks
(b) Construct a 95% confidence interval for each of the variables for good wine.     1 mark
(c) Find the mean of each of the variables for medium quality red wine. Do the same for the poor quality red wine.    1/2 mark
(d) Check if the means calculated for the medium and poor quality red wines fall within the corresponding confidence intervals of the good quality wine. For those attributes whose means lie outside the confidence interval, the attributes are significant in determining the quality.  This assumption is, however, partially compromised if the attribute fails the normality test. Identify the significant and non-significant variables, and comment.    1/2 mark

Good quality red wine
Alcohol    Residual sugar    Chlorides    Total sulfur dioxide    Density    pH    Sulphates    Citric acid
10    1.2    0.065    21    0.9946    3.39    0.47    0
9.5    2    0.073    18    0.9968    3.36    0.57    0.02
10.5    1.8    0.092    103    0.9969    3.3    0.75    0.56
9.7    2.1    0.066    30    0.9968    3.23    0.73    0.28
9.5    1.9    0.085    35    0.9968    3.38    0.62    0.16
10.5    1.8    0.065    16    0.9962    3.42    0.92    0.16
13    1.2    0.046    93    0.9924    3.57    0.85    0.08
10.3    1.4    0.056    24    0.99695    3.22    0.82    0.47
10.8    2.6    0.095    28    0.9994    3.2    0.77    0.74
10.8    2.6    0.095    28    0.9994    3.2    0.77    0.74
10.5    2.1    0.054    19    0.998    3.31    0.88    0.58
12.2    1.6    0.054    106    0.9927    3.54    0.62    0.04
9.2    2.2    0.075    24    1.00005    3.07    0.84    0.44
9.2    2.2    0.075    24    1.00005    3.07    0.84    0.44
10.5    2.6    0.085    33    0.99965    3.36    0.8    0.47
10.2    1.8    0.071    10    0.9968    3.2    0.72    0.52
12.8    3.6    0.078    37    0.9973    3.35    0.86    0.46
12.6    6.4    0.073    13    0.9976    3.23    0.82    0.45
10.5    5.6    0.087    47    0.9991    3.38    0.77    0.32
9.9    3.5    0.358    10    0.9972    3.25    1.08    0.68
10.5    5.6    0.087    47    0.9991    3.38    0.77    0.32
10.6    2.5    0.091    49    0.9976    3.34    0.86    0.09
10.6    2.5    0.091    49    0.9976    3.34    0.86    0.09
11.5    3.2    0.083    59    0.9989    3.37    0.71    0.39
11.5    3.2    0.083    59    0.9989    3.37    0.71    0.39
11.5    3.65    0.121    14    0.9978    3.05    0.74    0.66
11.7    2.5    0.078    38    0.9963    3.34    0.74    0.01
12.2    3.4    0.128    21    0.9992    3.17    0.84    0.53
9.8    2.3    0.082    29    0.9997    3.11    1.36    0.54
12.3    2.7    0.072    34    0.9955    3.58    0.89    0.02
11.7    2.95    0.116    29    0.997    3.24    0.75    0.66
10.4    3.1    0.109    23    1    3.15    0.85    0.66
10    5.8    0.083    42    1.0022    3.07    0.73    0.66
10    5.8    0.083    42    1.0022    3.07    0.73    0.66
12    2.4    0.074    18    0.9962    3.2    1.13    0.53
11.8    4.4    0.124    15    0.9984    3.01    0.83    0.71
12    2.4    0.074    18    0.9962    3.2    1.13    0.53
10    2.5    0.096    49    0.9982    3.19    0.7    0.31
12.9    1.4    0.045    88    0.9924    3.56    0.82    0.05
13    4.2    0.066    38    1.0004    3.22    0.6    0.76
10.8    3    0.093    30    0.9996    3.18    0.63    0.66
11.7    6.7    0.097    19    0.9986    3.27    0.82    0.53
11.8    2.4    0.089    67    0.9972    3.28    0.73    0.33
12.3    2.3    0.059    48    0.9952    3.52    0.56    0.03
11    2.1    0.066    24    0.9978    3.15    0.9    0.47
12.3    2.3    0.059    48    0.9952    3.52    0.56    0.03
11    2.1    0.066    24    0.9978    3.15    0.9    0.47
9.8    2.2    0.072    29    0.9987    2.88    0.82    0.72
11.2    3.7    0.1    43    1.0032    2.95    0.68    0.76
11.6    2.7    0.077    19    0.9963    3.23    0.63    0.49
12.5    1.7    0.054    27    0.9934    3.57    0.84    0.01
11.2    2.8    0.084    22    0.9998    3.26    0.74    0.63
13.4    5.2    0.086    19    0.9988    3.22    0.69    0.67
11.2    2.8    0.084    22    0.9998    3.26    0.74    0.63
11.7    2.8    0.08    17    0.9964    3.15    0.92    0.56
10.8    2.8    0.081    67    1.0002    3.32    0.92    0.55
13.3    2.5    0.055    25    0.9952    3.34    0.79    0.5
13.4    2.6    0.052    27    0.995    3.32    0.9    0.51
11    2.6    0.07    16    0.9972    3.15    0.65    0.53
11    2.6    0.07    16    0.9972    3.15    0.65    0.53
12    6.55    0.074    76    0.999    3.17    0.85    0.73
12    6.55    0.074    76    0.999    3.17    0.85    0.73
10.9    1.9    0.078    24    0.9976    3.18    1.04    0.47
10.8    1.8    0.077    22    0.9976    3.21    1.05    0.42
12.5    2.9    0.072    26    0.9968    3.16    0.78    0.63
10.8    1.8    0.075    21    0.9976    3.25    1.02    0.46
11.4    2.8    0.084    43    0.9986    3.04    0.68    0.75
11.8    2.4    0.107    15    0.9973    3.09    0.66    0.64
11.8    2.4    0.107    15    0.9973    3.09    0.66    0.64

Medium quality red wine
alcohol    residual sugar    chlorides    total sulfur dioxide    density    pH    sulphates    citric acid
9.4    1.9    0.076    34    0.9978    3.51    0.56    0
9.8    2.6    0.098    67    0.9968    3.2    0.68    0
9.8    2.3    0.092    54    0.997    3.26    0.65    0.04
9.4    1.9    0.076    34    0.9978    3.51    0.56    0
9.4    1.8    0.075    40    0.9978    3.51    0.56    0
9.4    1.6    0.069    59    0.9964    3.3    0.46    0.06
10.5    6.1    0.071    102    0.9978    3.35    0.8    0.36
9.2    1.8    0.097    65    0.9959    3.28    0.54    0.08
10.5    6.1    0.071    102    0.9978    3.35    0.8    0.36
9.9    1.6    0.089    59    0.9943    3.58    0.52    0
9.1    1.6    0.114    29    0.9974    3.26    1.56    0.29
9.2    3.8    0.176    145    0.9986    3.16    0.88    0.18
9.2    3.9    0.17    148    0.9986    3.17    0.93    0.19
9.3    1.7    0.368    56    0.9968    3.11    1.28    0.28
9.7    2.3    0.082    71    0.9982    3.52    0.65    0.31
9.5    1.6    0.106    37    0.9966    3.17    0.91    0.21
9.4    2.3    0.084    67    0.9968    3.17    0.53    0.11
9.3    1.4    0.08    23    0.9955    3.34    0.56    0.16
9.5    1.8    0.08    11    0.9962    3.28    0.59    0.24
9.5    1.6    0.106    37    0.9966    3.17    0.91    0.21
9.4    1.9    0.08    35    0.9972    3.47    0.55    0
10.1    2.4    0.089    82    0.9958    3.35    0.54    0.07
9.8    2.3    0.083    113    0.9966    3.17    0.66    0.12
9.2    1.8    0.103    50    0.9957    3.38    0.55    0.25
10.5    5.9    0.074    87    0.9978    3.33    0.83    0.36
10.5    5.9    0.074    87    0.9978    3.33    0.83    0.36
10.3    2.2    0.069    23    0.9968    3.3    1.2    0.22
9.5    1.8    0.05    11    0.9962    3.48    0.52    0.02
9.2    2.2    0.114    114    0.997    3.25    0.73    0.43
9.5    1.6    0.113    37    0.9969    3.25    0.58    0.52
9.2    1.6    0.066    12    0.9958    3.34    0.56    0.23
9.2    1.4    0.074    96    0.9954    3.32    0.58    0.37
9.2    1.7    0.074    23    0.9971    3.15    0.74    0.26
9.4    3    0.081    119    0.997    3.2    0.56    0.36
9.5    3.8    0.084    45    0.9978    3.34    0.53    0.04
9.6    3.4    0.07    10    0.9971    3.04    0.63    0.57
9.4    5.1    0.111    110    0.9983    3.26    0.77    0.12
10    2.3    0.076    54    0.9975    3.43    0.59    0.18
9.2    2.2    0.079    52    0.998    3.44    0.64    0.4
9.3    1.8    0.115    112    0.9968    3.21    0.71    0.49
9.8    2    0.081    54    0.9966    3.39    0.57    0.05
10.9    4.65    0.086    11    0.9962    3.41    0.39    0.05
10.9    4.65    0.086    11    0.9962    3.41    0.39    0.05
9.6    1.5    0.079    39    0.9968    3.42    0.58    0.11
10.7    1.6    0.076    15    0.9962    3.44    0.58    0.07
10.7    2    0.074    65    0.9969    3.28    0.79    0.57
9.5    2.1    0.088    96    0.9962    3.32    0.48    0.23
9.5    1.9    0.084    94    0.9961    3.31    0.48    0.22
9.6    2.5    0.094    83    0.9984    3.28    0.82    0.54
10.5    2.2    0.093    42    0.9986    3.54    0.66    0.64
10.5    2.2    0.093    42    0.9986    3.54    0.66    0.64
10.1    2    0.086    80    0.9958    3.38    0.52    0.12
9.2    1.6    0.069    15    0.9958    3.41    0.56    0.2
9.4    1.9    0.464    67    0.9974    3.13    1.28    0.7
9.1    2    0.086    73    0.997    3.36    0.57    0.47
9.4    1.8    0.401    51    0.9969    3.16    1.14    0.26

Poor quality red wine
alcohol    residual sugar    chlorides    total sulfur dioxide    density    pH    sulphates    citric acid
9    2.2    0.074    47    1.0008    3.25    0.57    0.66
8.4    2.1    0.2    16    0.9994    3.16    0.63    0.49
10.7    4.25    0.097    14    0.9966    3.63    0.54    0
9.9    1.5    0.145    48    0.99832    3.38    0.86    0.42
11    3.4    0.084    11    0.99892    3.48    0.49    0.02
10.9    2.1    0.137    9    0.99476    3.5    0.4    0
9.8    1.2    0.267    29    0.99471    3.32    0.51    0
10.2    5.7    0.082    14    0.99808    3.4    0.52    0.05
9.95    1.8    0.078    12    0.996    3.55    0.63    0.02
9    4.4    0.086    29    0.9974    3.38    0.5    0.08
9.8    1.5    0.172    19    0.994    3.5    0.48    0.09
9.3    2.8    0.088    46    0.9976    3.26    0.51    0.3
13.1    2.1    0.054    65    0.9934    3.9    0.56    0.15
9.2    2.1    0.084    43    0.9976    3.31    0.53    0.26
9.1    1.5    0.08    119    0.9972    3.16    1.12    0.2
10.5    1.4    0.045    85    0.9938    3.75    0.48    0.04
9.4    3.4    0.61    69    0.9996    2.74    2    1
9.2    1.3    0.072    20    0.9965    3.17    1.08    0.02
9    1.6    0.072    42    0.9956    3.37    0.48    0.03
9.1    1.8    0.058    8    0.9972    3.36    0.33    0.03
11.4    2.1    0.061    31    0.9948    3.51    0.43    0.06
10.4    2    0.089    55    0.99745    3.31    0.57    0.36
9.4    2    0.087    67    0.99565    3.35    0.6    0.04
9.8    3.3    0.096    61    1.00025    3.6    0.72    0
9.6    4.5    0.07    49    0.9981    3.05    0.57    0.49
9.6    2.1    0.07    47    0.9991    3.3    0.56    0.49
10    2.3    0.103    14    0.9978    3.34    0.52    0.24
10    2.1    0.088    23    0.9962    3.26    0.47    0.27
11.3    3.4    0.105    86    1.001    3.43    0.64    0.22
11    2.2    0.07    14    0.9967    3.32    0.58    0.01
11    4.4    0.096    13    0.997    3.41    0.57    0.02
9.6    2.6    0.073    84    0.9972    3.32    0.7    0.48
9.7    1.6    0.078    14    0.998    3.29    0.54    0.04
11.2    3.1    0.086    12    0.9958    3.54    0.6    0.1
11.4    2.1    0.102    7    0.99462    3.44    0.58    0.24
10.9    2.5    0.058    9    0.99632    3.38    0.55    0.07
9.9    1.6    0.147    51    0.99836    3.38    0.86    0.44

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