Assessment item 2—Assignment 2 Complete Solution

Question: #8757

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 (since the assignment must be submitted electronically as a single file) and an appropriate equation editor should be used. Important note: There is no need to include the text of the assignment questions in your submission.
•   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.
•   For those questions where Excel is not used, 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.
•   There will be late submission penalty for submissions beyond the deadline unless prior approval is obtained from the Course Coordinator through the extension system in Moodle. Under no circumstances any submission that is late beyond 14 days from the deadline 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 “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.   1 mark
(b)   Construct a relative frequency histogram for these data with equal class intervals, the first class being “$0 to less than $5”.                            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 interval size is doubled, which means the first class will be “$0 to less than $10”?                                   1 mark
(d)   What proportion of stock prices were above $25?                   1 mark
(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   4 Marks
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.   1 mark
(b)   Compute the standard deviation, range and coefficient of variation from the sample data for each state.   1 mark
(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.     1mark
(d)   Compare the box plots and comment on the skewness 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 mental and behavioural problems of Australian residents. (You can get the data from Table 3 from the URL: http://www.abs.gov.au/AUSSTATS/abs@.nsf/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?                           1 mark
(b)   What is the probability that a person, randomly selected, belongs to the age group of 55 or over?                                           1 mark
(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?                           1 mark
(d)   Are different types of mental and behavioural problems independent of the gender?   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 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?    1 mark
(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).     1 mark

(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?    1 mark
(ii) What is the amount of rainfall if only 8% of the weeks have that amount of rainfall or higher?   1 mark

Question 5   4 Marks
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. 2 marks
(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. 2 marks

Solution: #8783

Assessment item 2—Assignment 2 Complete Solution

Step 2: then select the ‘Data’ option in menu bar Step 3: select ‘Data Analysis’ option available...