Statistical Analysis of Unleaded 91 Fuel Prices in Queensland

This project covers the statistical analysis of Unleaded 91 fuel prices in Queensland on September 11, 2018. It includes hypothesis testing and conclusions based on the results.

SOUTHERN CROSS UNIVERSITY
School of Business and Tourism
MAT10251 Statistical Analysis
PROJECT COVER SHEET
Please complete all of the following details and then make these sheets the first pages of
your project – do not send it as a separate document.
Your project must be submitted as a Word document.
PART B
Student Name: Selven Armoogum
Student ID No.: 22459299
Tutor’s name: Mr Badri
Due date:
Date submitted:
Declaration:
I have read and understand the Rules Relating to Awards (Rule 3 Section 18 –
Academic Integrity) as contained in the SCU Policy Library. I understand the
penalties that apply for academic misconduct and agree to be bound by these
rules.
The work I am submitting electronically is entirely my own work.
.
Signed: S.Armoogum
Date:

STUDENT NAME: S.Armoogum
STUDENT ID NUMBER: 22459299
MAT10251 – Statistical Analysis
Project Part B
Enter your sample number below
Sample Number (last digit of your student ID number) 9
Fuel
First letter family name A to M – Unleaded 91
First letter family name N to Z – Diesel
Unleaded 91
(A)

Value: 5%

Marking and Feedback Sheet Part B
Max Marks Mark
Cover sheet or sample incorrect -2
Format incorrect, including file name -2
Self-Marking and Reflection Part A (5 marks)
Self-Marking Part A 2
Reflection 3
Part B Statistical Inference Tasks (19 marks)
Statistical Inference Question 1
Choice of technique, assumptions & other required steps 4
Calculation (Excel output) 3
Conclusion 2
Statistical Inference Question 2
Choice of technique, assumptions & other required steps 5
Calculation (Excel output) 3
Decision and conclusion 2
Written task - Discussion and results (6 marks)
Question 1 2
Question 2 2
Structure, grammar and spelling 2
Total Part B 30 0.0
Comments

Introduction
The objective of this task is to answer two research questions related to the prices of
Unleaded 91 in Queensland with a focus on September 11, 2018. Two research questions
were sought to be answered and they focused on testing whether the prices of Unleaded 91 in
Queensland were expensive on September 11, 2018. The research questions are;
a) Was the average price of the Unleaded 91 fuel for the given sample expensive on
September 11, 2018 Queensland state?
b) On September 11, 2018 was the price of Unleaded 91 for the given sample at least
$1.50 per litre in more than 25% of petrol stations in Queensland?
Results and Analysis
We begin by testing the first research question which is;
a) Was the average price of the Unleaded 91 fuel for the given sample expensive on
September 11, 2018 Queensland state?
The average price of the Unleaded 91 fuel in Queensland on September 11, 2018 was $1.58
per litre. So to answer the research question, the following hypothesis was tested;
H0: The average price of the Unleaded 91 fuel in Queensland on September 11, 2018 is equal
to 158 cents ($1.58) per litre.
HA: The average price of the Unleaded 91 fuel in Queensland on September 11, 2018 is
greater than 158 cents ($1.58) per litre.
To test this hypothesis, a One-sample t-test was performed at 5% level of significance.
The results of the first hypothesis tested are given in table 1 below.

Table 1: t-Test: Two-Sample Assuming Equal Variances
Unleaded 91
(Cents per Litre)
Average price
(Cents per Litre)
Mean 157.6363 158
Variance 29.12487 0
Observations 80 80
Pooled Variance 14.56244
Hypothesized Mean
Difference 0
df 158
t Stat -0.60286
P(T<=t) one-tail 0.273733
t Critical one-tail 1.654555
P(T<=t) two-tail 0.547467
t Critical two-tail 1.975092
As can be seen from the above results, the average price of Unleaded 91 in the sample that
was provided is 157.64 (Cents per Litre) while the average in Queensland state was 158
(Cents per Litre). The p-value of the test was 0.2737 (a value greater than 5% level of
significance), we therefore fail to reject the null hypothesis and conclude that the average
price of the Unleaded 91 fuel in Queensland on September 11, 2018 is equal to 158 cents
($1.58) per litre. Based on the results we can conclude that the average price of the Unleaded
91 fuel for the given sample was not expensive on September 11, 2018 Queensland state.
Next we test the second research question which is;
a) On September 11, 2018 was the price of Unleaded 91 for the given sample at least
$1.50 per litre in more than 25% of petrol stations in Queensland?
To answer the research question, the following hypothesis was tested;
H0: The average price of the Unleaded 91 fuel was at least $1.50 in 25% of petrol stations in
Queensland.

HA: The average price of the Unleaded 91 fuel was at least $1.50 in more than 25% of petrol
stations in Queensland.
To test this hypothesis, a One-sample t-test for proportions was performed at 5% level of
significance.
The results of the second hypothesis tested are given in tables 2 and 3 below.
Table 2: One-Sample Statistics
N Mean Std. Deviation Std. Error Mean
Is the price of Unleaded 91
fuel at least $1.50 per litre?
80 .8625 .34655 .03875
Table 3: One-Sample Test
Test Value = 0.25
t df Sig. (2-
tailed)
Mean
Difference
95% Confidence Interval of
the Difference
Lower Upper
Is the price of
Unleaded 91 fuel at
least $1.50 per litre?
15.808 79 .000 .61250 .5354 .6896
From the above results, we can observe that the average proportion of petrol stations with
price of the Unleaded 91 fuel being at least $1.50 was 86.25%. The p-value is 0.000 (a value
less than 5% level of significance), we therefore reject the null hypothesis and conclude that
the average price of the Unleaded 91 fuel was at least $1.50 in more than 25% of petrol
stations in Queensland. Based on these results, we can conclude that the price of Unleaded 91
fuel was expensive on September 11, 2018 for the Queensland state.

Conclusion
Based on the above analysis, it is clear that the sample fuel prices in the 80 selected petrol
stations was not greater than the average for the Queensland state. However, considering
whether the prices of Unleaded 91 were more than $1.50 per litre results showed that about
86.25% of the petrol stations had prices of Unleaded 91 greater than or equal to $1.50 per
litre. This therefore can be said to be very expensive if the baseline is $1.50 per litre.

Appendices Part B Definition of random variable/s
The random variable included is the price of unleaded 91 fuel that is a continuous variable. Any required assumptions.
The assumptions taken for the analysis of one-sample t-test is that the variable is normally
distributed and that the values were randomly selected. Why test or interval was chosen
One-sample t-test was chosen because there is only one variable to be tested.
Hypotheses Hypotheses and decision for a hypothesis test
H0: The average price of the Unleaded 91 fuel in Queensland on September 11, 2018 is equal
to 158 cents ($1.58) per litre.
HA: The average price of the Unleaded 91 fuel in Queensland on September 11, 2018 is
greater than 158 cents ($1.58) per litre.
H0: The average price of the Unleaded 91 fuel was at least $1.50 in 25% of petrol stations in
Queensland.
HA: The average price of the Unleaded 91 fuel was at least $1.50 in more than 25% of petrol
stations in Queensland.
 Excel output
Table 1: t-Test: Two-Sample Assuming Equal Variances
Unleaded 91
(Cents per Litre)
Average price
(Cents per Litre)
Mean 157.6363 158
Variance 29.12487 0
Observations 80 80
Pooled Variance 14.56244
Hypothesized Mean
Difference 0
df 158
t Stat -0.60286
P(T<=t) one-tail 0.273733

t Critical one-tail 1.654555
P(T<=t) two-tail 0.547467
t Critical two-tail 1.975092
 Interpretation of results and a conclusion
As can be seen from the above results, the average price of Unleaded 91 in the sample that
was provided is 157.64 (Cents per Litre) while the average in Queensland state was 158
(Cents per Litre). The p-value of the test was 0.2737 (a value greater than 5% level of
significance), we therefore fail to reject the null hypothesis and conclude that the average
price of the Unleaded 91 fuel in Queensland on September 11, 2018 is equal to 158 cents
($1.58) per litre. Based on the results we can conclude that the average price of the Unleaded
91 fuel for the given sample was not expensive on September 11, 2018 Queensland state.
 Excel output
t-Test: Two-Sample Assuming Equal Variances
Variable
1
Variabl
e 2
Mean 0.8625 0.25
Variance 0.120095 0
Observations 80 80
Pooled Variance 0.060047
Hypothesized Mean
Difference 0
df 158
t Stat 15.80843
P(T<=t) one-tail 1.16E-34
t Critical one-tail 1.654555
P(T<=t) two-tail 2.32E-34
t Critical two-tail 1.975092
 Interpretation of results and a conclusion
From the above results, we can observe that the average proportion of petrol stations with
price of the Unleaded 91 fuel being at least $1.50 was 86.25%. The p-value is 0.000 (a value
less than 5% level of significance), we therefore reject the null hypothesis and conclude that

the average price of the Unleaded 91 fuel was at least $1.50 in more than 25% of petrol
stations in Queensland. Based on these results, we can conclude that the price of Unleaded 91
fuel was expensive on September 11, 2018 for the Queensland state.