QUANTITATIVE METHODS FOR BUSINESS
MATH1053

Assignment 2: Due Saturday January 11 at 23:00
Submission

Any assignments are to be submitted via a submission link on the Module ASSESSMENT tile in
electronic (typed in WORD or EXCEL) format. Any submission handed to your teacher in paper form
or email will not be accepted without prior approval. Assignments submitted late, without an
extension being granted, will attract a penalty of 10% per day to a maximum for 3 days beyond the
due date/time. No submission is allowed after the cut-off. Please refer to the Module Information
Booklet for the policy regarding extensions.
The submission will consist of two files, your primary word document containing all the working and
evidence and an Excel spreadsheet file however any relevant information (tables and diagrams) must
be copied (snipping tool) from the excel file into the word document. The spreadsheet file is for
academic integrity validation only (check that you did your own work).

Presentation

Make sure that the pages of your submission are in the correct order and each page shows your
name, student ID and page number. Poor presentation, including layout of formulae and/or
explanations of the process, will attract a maximum penalty of 10%. Use of Microsoft Equation Editor
3.0 is encouraged. For this assignment you must show all your work, including formulae used,
explanation of variables, together with a discussion on the process employed. All steps of the process
must be shown. Any items omitted will result in loss of marks. Do not copy the whole original
question as part of your submission. You may provide you own question introduction.

Declaration / Plagiarism

Attach a plagiarism declaration cover sheet (download from Student Lounge > Documents and
Forms).

Plagiarism is the use of another persons ideas (and words) without saying where you got the
information the taking and using as ones own the thoughts, writings or inventions of another. The
Shorter Oxford English Dictionary on historical principles, Onions CT, 3rd ed. The lack of in-text
references together with a reference list will, may result in zero marks for the section in question.
The copying (even partially) of another persons work may result in both people receiving zero marks.
Contract cheating occurs when student presents work as their own that has been knowingly
completed for them by another party (or parties) either gratuitously or in return for payment or
generated through Artificial Intelligence.
For further details please see Academic Integrity Tab on the Student Lounge. Assignments will be
processed through TurnItIn to check for plagiarism. Your submission of the assignment indicates your
acceptance to having your paper checked in this way and a potential Viva-voce (interview)
afterwards.

Support

Helpful videos and Excel examples are located in the ASSESSMENT:   Preparing Assignment Using MS
EXCEL (videos). Otherwise contact your lecturer or attend / request a Zoom session.

Marking and Feedback

Total marks per question are provided. A breakdown of each question in parts will show the
allocation of marks and specifically where marks were lost. Where to find more opportunities to
practice additional background theory may be provided.

Online Documents
 Weblink

 Spreadsheet 1: Business turnover indicator, change in turnover, seasonally adjusted.xlsx

 Spreadsheet 2: 5681001_13-industry_summary.xlsx

Question 1: Descriptive statistics 33 Marks

a) (4 marks) Identify the data/variables have been collected (Spreadsheet 1 or 2) and classify them
as ordinal, nominal, discrete, or continuous. Present your classification results in a table.
Hint: there are at least three variables

Data 1 sheet within the spreadsheet of Spreadsheet 2 contains a
collection of 178 months (from Jan. 2010 to Oct. 2024) of business
turnover indices (BTI) across 42 different industries.
Use the simple random sample method to select one month from the data and answer the following
questions:

b) (2 marks) Detail the steps how the month was selected randomly.
c) (3 marks) Prepare a descriptive statistics table using Excel for that month  s BTI
d) (4 marks) Using 1.5IQR rule to identify the outliers.
e) (4 marks) Generate a frequency distribution table with 6 intervals. The lowest class boundary
must be the minimal of the BTI. The table must contain the following columns   frequency  ,
  frequency in percentage  ,   cumulatively frequency  , and   cumulatively frequency in percentage  .
f) (4 marks) Create a labelled histogram using Excel based on the frequency distribution table
generated in e).
g) (4 marks) Briefly describe the shape of the distribution (i.e. symmetry, modality)
h) (4 marks) Which measures of central tendency should you use? What is its value? Give a brief
explanation of the reason for your choice.
i) (4 marks) Which measures of dispersion should you use to? What is its value? Give a brief explanation
of the reason for your choice.

Question 2: Linear correlation 25 Marks
In Spreadsheet 2   Data 1  , analyse the relationship between   Construction (COL E)   and   Wholesale trade
(COL F)  
a) (3 marks) Determine the independent and dependent variables and explain the reason.
b) (6 marks) Create a labelled scatter plot (appropriate scale, axis labelling and student ID as a part of the
title) for these two variables. Show the line of the best fit, display the equation and R-squared value on
the scatter plot.
c) (6 marks) Interpreter the following parameters using your model created in c):
1. the slope of the linear model
2. the y-intercept of the linear model
3. the coefficient of determination

d) (4 marks) Use the linear model to calculate all the residuals. Show your results in a new EXCEL sheet.
e) (3 marks) Create a residual plot (appropriate scale, axis labelling and student ID as a part of the title).
f) (3 marks) Discuss the appropriateness of the model. You must provide the reason(s) and sufficient
evidence(s) to support your statement.

Question 3: Empirical Probability 13 Marks

A group of students conducted a survey to investigate the common NBN plans (speed) and service providers used
by university students. 550 students were asked, and the results are listed in Table 1 below.

Table. 1 Survey result for the NBN plans
Service providers
NBN plans Optus TPG Internode Vodafone Total
Basic (12Mbps) 10 30 16 ** 146
Standard (25Mbps) 27 15 38 60 140
Premium (100Mbps) 6**2 10 132 264
Total 97 107 64 282 550

Answer the following questions using Table. 1, ensuring you show the probability statement for each part.
a) (2 marks) What is the probability that a survey respondent is using TPG?
b) (2 marks) What is the probability that a survey respondent is not on a Premium plan?
c) (2 marks) What is the probability that a survey respondent is using Optus or on a Standard plan?
d) (2 marks) What is the probability that a survey respondent is using Internode given he/she on a Basic
plan?
e) (5 marks) Are the two events, Service providers and NBN plans, statistically independent?
Evaluate using Premium and Vodafone categories.

Question 4: Normal Distribution 34 Marks
a) Research indicates that the CO2 Emissions for different vehicles follow a normal distribution with
a mean of 248 g/km and a standard deviation of 18 g/km. Use the given information answer the
following questions (show all steps and probability statement):
I. (5 marks) What is the probability that the CO2 Emissions exceed 270.05 g/km?
II. (4 marks) What is the probability that the CO2 Emissions between 221.9g/km and 270.05
g/km?
III. (4 marks) To be in the lowest 10% of all vehicles, the CO2 emissions must be below what
value?
IV. (2 marks) Provide a clearly labelled diagram for III) (You can use Normal Distribution
(onlinestatbook.com) to draw the curve)
b) (6 marks) Download the CO2.csv from the assignment page and produce a histogram using EXCEL
for the CO2 Emissions(g/km) column. Describe the shape of this histogram(distribution). Based
on your observations, do you believe the CO2 Emissions follow a normal distribution? Provide a
detailed explanation to support your conclusion.
c) (6 marks) Clearly the CO2.csv is a sample dataset, calculate the sample mean and sample
standard deviation using EXCEL for this dataset. Then find the 95% confidence interval for the
population mean. Interpret the meaning of the confidence interval.
d) (2 marks) Compare the result in c) with the population mean provided in a) and draw a
conclusion.

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