Assessment details for all students

Assessment item 2—Assignment 2

Due date: 6:00pm, Friday Week 10 ASSESSMENT

Weighting: 20%

2Format: 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).

Excel may be used to assist in statistical calculations for questions in this assignment. Where Excel is used, the name of the Excel functions should be included and output printout should be pasted.

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.

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).

PlagiarismCQU values academic honesty. Consequently, plagiarism will not be tolerated in assessment items. This assignment must be completed by each student individually.

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Question 1 4 Marks

Visit the Australian Stock Exchange website, www.asx.com.au and from “Browse top companies”, select “BHP BLT” (BHP Billiton). On BHP Billiton webpage near the bottom where there is a price history chart, select more charting options (where it says *More charting options are available.), select Timeframe as “Monthly Prices over 10 years”. After you create the chart, read the values in the beginning of every Quarter (January, April, July, October) for every year from 2005 to 2013.

(a) Construct a stem-and-leaf display for these data. 1 mark

(b) Construct a relative frequency histogram for these data with the same number of columns as the number of stems in the stemplot. 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 number of columns in the histogram is halved?

1 mark

(d) What proportion of stock prices were above $35? 1 mark

(Note: If you get the prices from any other source, such as Etrade, Australia as given in the figure below, use the opening price for the given month. As you move the bar in the interactive chart, the values will display in dollars and cents. Ignore the cent values and only work with whole dollars.)

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Question 2 4 Marks

EPA has estimated highway mileage for selected US automobile makers. The following information, each value is the performance of each car tested, is provided from their records:

Make Miles per gallon

Buick: 31 28 27 30 27 25 31

Chevrolet: 34 27 26 34 28 25 28

Dodge: 36 32 26 26 34 32 24

Ford: 36 42 25 29 31 29 33 27

(a) Compute the mean, median, first quartile, and third quartile for each make 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 company. 1 mark

(c) Draw a box and whisker plot for each company and put them side by side on the same scale so that their performances can be compared. 1mark

(d) Compare the box plots and describe 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 Australians on Households tenure by type of household. (Catalogue Number 1319.0 – Australian Housing in Brief, 1998).

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(a) What is the probability that a randomly selected dwelling is owner-occupied irrespective of whether the owner has a mortgage or no mortgage? 1 mark

(b) What is the probability that a dwelling, given that it is rented as a private property, selected at random, is occupied by a Lone person? 1 mark

(c) What proportion of households are couple only? 1 mark

(d) Are the characteristics ‘Couples or not couples’ and ‘Owners or renters or rent-free’ independent of each other? 1 mark

Question 4 4 Marks

(a) The following data collected from the Australian Bureau of Meteorology website (http://www.bom.gov.au/climate/dwo/IDCJDW3050.latest.shtml) gives the daily rainfall data for one year in Melbourne (recorded in mm at Tullamarine Airport). The blank values indicate no rainfall. 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 3 or more days of rainfall in a week? (There are 52 weeks in a year). 2 marks

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Date Jun-14 May-14 Apr-14 Mar-14 Feb-14 Jan-14 Dec-13 Nov-13 Oct-13 Sep-13 Aug-13 Jul-131 2 0.22 7.8 0.2 4.8 0.2 1.63 3.2 0.6 1.44 3 0.6 9 1.4 0.45 5.2 10.8 7.6 17 0.46 0.8 1 1.4 3.2 6.27 1.2 3 0.88 1 15.8 4.49 14.8 3.6 0.2 6.410 0.4 18.611 12.8 13.4 8 4.2 0.212 13.2 2.2 2.4 1 2.413 5.8 20 2 1.614 1 7.8 5.415 0.2 2.6 1.2 1816 2.4 3.217 2.2 5.8 14.8 1.2 1.8 23.818 0.819 10.4 0.6 720 9.4 0.4 1.8 0.621 0.2 0.222 1.6 8.4 0.4 2023 4.6 6.6 2.6 16 2.4 3.2 3.224 4.6 0.6 4.4 0.6 1.2 2.4 6.425 6.2 0.8 12 0.626 0.6 0.6 33.6 0.4 0.627 4.4 0.2 1.428 2 7.8 1.829 4.6 8.4 3.4 530 11.2 13.4 0.2 2.4 3.6 2.231 0.8 1

(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 5 mm and 15 mm of rainfall? 1 mark

(ii) What is the amount of rainfall if only 2% of the weeks have that amount of rainfall or higher? 1 mark

Question 5 4 Marks

Barley is widely grown in Australia. The total area cultivated for barley in Australia is higher than any other crop except wheat. In 2012, barley was cultivated in 3.740 million hectares (mha) compared to 13.645 mha for wheat, 2.093 mha for Canola, 0.544 mha for cotton, 0.292 mha for sugarcane, and 0.075 mha for rice.

(a) The area under barley cultivation in different years is provided by the Australian Bureau of Statistics as given in the table below. Can the variable Area be considered as normally distributed? (Ignore the time series nature of the data.). Support your decision through the use of appropriate statistics and graphs. 2 marks

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(b) Assuming that the variable Area is normally distributed, find its 95 percent confidence interval.

2 marks

Table: Yearwise barley cultivation area in million hectares for the whole of Australia.

(Source: Australian Bureau of Statistics, Catalogue No. 7121.0)

Year Area

1998 3.56

1999 3.20

2000 2.60

2001 3.45

2002 3.66

2003 3.81

2004 4.42

2005 4.60

2006 4.41

2007 4.18

2008 4.90

2009 5.02

2010 4.42

2011 3.68

2012 3.74

2013 3.62

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