Question 1.
Explain the following, illustrating your explanation with examples and diagrams where necessary:
- Scatter diagram
- Correlation of r = 0
- Line of best fit
- The difference between positive and negative correlation
Question 2.
The financial reports of Brisbane North Pty Ltd and Brisbane South Pty Ltd disclosed the following profits for last five years. Both companies manufacture the same product.
|
Year
|
Brisbane North P/L
|
Brisbane South P/L
|
|
2011
|
$250,000
|
$110,000
|
|
2012
|
$310,000
|
$170,000
|
|
2013
|
$450,000
|
$250,000
|
|
2014
|
$650,000
|
$470,000
|
|
2015
|
$890,000
|
$550,000
|
Assessment task:
A. Draw a scatter diagram and analyse and explain your analysis
B. Calculate and discuss the correlation coefficient of the two companies using the product moment method
C. If Brisbane North P/L makes a profit of $750 000, estimate the profit for Brisbane South P/L using:
o A line of best fit through the scatter diagram
o A line of best fit using the least-squares method
Question 3.
Outline sources of relevant information available to the financial services industry and briefly explain their relevance to the industry.
Question 4.
Explain the following terms, illustrating your explanation with examples where necessary:
- Non-sampling error
- Primary data
- Random sampling
- Multistage sample
- Stratified sample
Question 5.
The following table shows the average award rates of pay and consumer price index of Superland.
|
Year
|
Weekly Award Wage
$
|
Consumer Price Index
(2005-6 =100)
|
|
June 2005
|
250.00
|
97.2
|
|
June 2006
|
265.00
|
103.5
|
|
June 2007
|
285.00
|
110.0
|
|
June 2008
|
310.00
|
112.0
|
|
June 2009
|
320.00
|
114.7
|
|
June 2010
|
335.00
|
125.3
|
|
June 2011
|
350.00
|
131.6
|
|
June 2012
|
365.00
|
139.0
|
Assessment task:
- Prepare a spreadsheet with columns for Year, Weekly Award, CPI, Real Weekly Award and Revised CPI
- Using the price index given, calculate real weekly award wages for each year for 2005-06 prices, round up to the nearest cent.
- Calculate an index for weekly award wages using June 2005 as the base year, round up to the nearest cent.
Question 6.
The following sales data have been extracted from Brisbane North Pty Ltd for the years 2006 to 2013.
|
Year
|
Sales (Y)
|
|
2006
|
17,000
|
|
2007
|
17,500
|
|
2008
|
18,200
|
|
2009
|
19,000
|
|
2010
|
19,500
|
|
2011
|
20,100
|
|
2012
|
20,500
|
|
2013
|
21,000
|
Assessment task:
Prepare a spreadsheet showing Exponential Smoothing of the data with a smoothing constant of 45%.
Question 7.
Standard deviation is commonly used by businesses to measure confidence in statistical conclusions. Unlike the variance, the standard deviation is expressed in the same units as the data.
Assessment task
Explain the standard deviation and how it is used in business. Illustrate your explanation by examples and application in some industries.
Question 8.
History students scored an average of 82% in their final exam. Assuming a normal curve with a standard deviation of 5%:
(i) What is the probability of a student scoring less than 50%?
(ii) (ii) What percentage of students scored higher than 75%?
(iii) (iii) What percentage of students scored between 60% and 75%?