KOI University BUS708: Statistical Modelling of Fuel Prices Report

This report presents a statistical analysis of fuel prices and their impact on consumer choices, based on data from various service stations. The analysis includes descriptive statistics, graphical displays (histograms, box plots, and pie charts), and hypothesis testing to determine the distribution of fuel prices, compare prices across different brands, and assess whether average prices exceed a certain threshold. The study uses both secondary data from government sources and primary data collected through a survey at KOI University. The report investigates the relationship between fuel prices and market share, concluding that price significantly influences consumer decisions. Key findings include comparisons of major brands (Caltex, Coles Express, 7-Eleven, and Caltex Woolworths), and the identification of statistically significant price differences among them. The report also examines the preferences of students at KOI University regarding fuel service providers. The report provides a comprehensive overview of the fuel market and provides valuable insights for NRMA to prepare for media reports.

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Name:
Institution Affiliate:
Title

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Contents
Executive summary.....................................................................................................................................3
Section (1): Introduction..............................................................................................................................3
Section (2a): What is the shape of the distribution of the variable Price?...................................................4
Section (2b): Is the average price of petrol is in all service station in September 2016 is more than 115
Australian cents?.........................................................................................................................................5
Section (3a): Give numerical summary and appropriate graphical display for comparing the price of
petrol of those four major Brands...............................................................................................................6
Section (3b): Perform a suitable hypothesis test at a 5% level of significance to test whether there a price
difference among these four major Brands.................................................................................................8
Section 4: Sample survey at KOI University.................................................................................................8
Conclusion...................................................................................................................................................9
References.................................................................................................................................................10

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Executive summary
Fuel price economy is perhaps one of the most imperative overlooked factors that determine
consumers’ choice of fuel service provider. Research has shown that fuel price is indeed a major factor
that influence fuel consumer’s choice. However some studies argue that fuel quality and service trump
the influence of prices on choice of consumers. The aim of the study was to investigate whether fuel
prices have a significant influence on choice of the consumer on the fuel service provider. Analysis
carried on historical fuel prices data and service providers indicated that fuel prices had indeed a
significant relationship with consumer choice of service providers. The study found the biggest fuel
market owner had the lowest prices and also the lowest price fluctuations. Caltex and seven eleven
owned more than half of the market share with a market with a mean price of 122.6 compared on the
overall mean price of 123.3.
Section (1): Introduction
Fuel is a highly consumed commodity across the globe especially in the developed nations
(Hinterhuber, 2015). Although there are complaints from its detrimental effect on the environment, the
demand for fuel continues to grow. This can be attributed to the population increase, globalization and
the individual’s increased interest in owning personal mode of transport. High demand for fuel attracts
many fuel service providers. There are a number of factors that affect the one’s choice of fuel service
providers such as service quality (Klaus & Maklan, 2013), proximity, fuel and lastly and arguably the
most important is the fuel price (Li, Shen, Wang & Jiang, 2016). More established service providers
are able to sell fuel at lower prices to attract more consumers thus maintaining a large market share
(Liu-Thompkins & Tam, 2013). In this discussion the effect of price on the demand of fuel based on the
price in eight different fuel services providers in Australia is invested and discussed. The aim of the
research was to find whether fuel prices has a significant effect on the consumers’ choice of service
provider. The investigation further focuses on the four major fuel providers in Australia to further
investigate their market share and compare it to the fuel prices offered by the service providers.
The first dataset comprised of eight service station fuel price history located in Australia. The
dataset was collected from Australian government and thus secondary and was contained of six
variables (ckbarth & Madlener, 2016). Five of the variables were explanatory variable and one was the
response .The first explanatory variable was service station name which was a string variable. Second
and third explanatory variables were fuel stations’ address and suburb and were also a string variable.
Fourth explanatory variable in the dataset was the postal code of the sampled fuel station and its data
type was numeric. The fifth explanatory variable in the dataset was fuel code, the variable was
categorical dataset and comprised of the different types of fuel sold at the fuel stations under study. The
fifth and final variable under study was the fuel prices, the variable was the response variable of the
study and its data type was numeric. The data is suitable to carry may be used to investigate fuel prices
in various suburbs and preferred brands different in various suburbs. (Yeung, 2013)
The second dataset was composed of primary data. The data was collected by conducting a
survey on 30 students from King’s Owen University. Interviews method was used in the study to collect
quantitative data. Random sampling method was used in the selecting the population sample.
Individuals that did not buy fuel from any fuels station were disregarded. The collected dataset
contained two variables. The first variable was students’ number which was a numeric datatype and

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represented the students sampled in the survey. The variable was the explanatory variable in the study.
The other variable wad the students preferred brand of fuel service provides. This was the response
variable in the study and its data was numeric. There was however some limitations that were identified
in the survey. Firstly the sample size of thirty was significantly small therefore the data may have been
biased. Secondly, the individuals sampled in the survey was from a relatively small geographical area.
This may have also contributed to biasness of the data. (Van-Vliet, Shove & Chappells, 2012).
Section (2a): What is the shape of the distribution of the
variable Price?
The shape of the distribution of the price variable was investigated using descriptive statistics,
histogram and box and whisker plot (Stevens, 2010). Excel Analytics was used in the conducting the
hypothesis test and the results were as displayed in the table 1 below.
Table 1
Price
Mean 123.3709
Standard Error 0.403144
Median 123.9
Mode 129.9
Standard Deviation 12.74853
Sample Variance 162.5249
Kurtosis -0.18395
Skewness 0.101395
Range 106.7
Minimum 78.9
Maximum 185.6
Sum 123370.9
Count 1000
The mean of the price of fuel in all the fuel station services was 123.4 Australian cents. The
mode or the most occurring price of fuel across all sampled fuel providers was 129.9 The minimum and
the maximum fuel prices across all the fuel service providers was 78 and 185.6 Australian cents
respectively. The data had a skewness of 0.101395 and kurtosis of the data was -0.18395. The measure
of dispersion of the data, range and standard deviation, were 106.7 and 12.7 respectively.

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95
105
115
125
More
0
100
200
300
0.00%
40.00%
80.00%
120.00%
Histogram
Frequency
Cumulative %
Bin
Frequency
From the histogram of the fuel price data distribution it is apparent that the data frequency of
the data increases with increase in price. Thus the data is left tailed or skewed to the left. (Lovelock &
Patterson, 2015).
Section (2b): Is the average price of petrol is in all service
station in September 2016 is more than 115 Australian
cents?
To determine the answer to the question, a hypothesis was formulated and t-test analysis
conducted to determine the truthfulness of the assertion. ( Gu, 2013).
H0: The average price of fuel in all petrol stations is less equal or less than 115 Australian cents.
H1: The average price of fuel in in all petrol stations is more than 115 Australian Cents.
The test has four major assumptions
1. The response variable should be continuous
2. Observations should be self-reliant.
3. Response variable should not have any outlier.
4. The explanatory variable should be nearly normally distributed. (Fay & Proschan, 2010).

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Hypothesis Test for μ (Mean)
Hypotheses
H0 μ ≤ 115
H1 μ > 115
Type of test Lower than
Significance level
α 0.05
Critical Region
D. F 999
Critical Value 1.6464
Sample Data
Sample Deviance 12.7485
Sample Average 123.3709
Size of Sample 1000
S.E Mean 0.4031
t Statistic 20.76405
p-value 0.0000
Decision
Reject H0
One tailed test was conducted using 95% confidence interval with the T-test statistic of 1.6464.
Two methods were used to arrive at the same decision. The first method was using T–sample statistic
which was 20.8 and larger than the critical value 1.6464 at 95 level of confidence thus the null
hypothesis is not accepted (Colicchia, Marchet, Melacini, & Perotti, 2013). The second method was
using p-value of the test which was at 0.0 and less than 0.05 at 95% significance level thus the null
proposition is not accepted. From the hypothesis test we then hypothesis is rejected and therefore the
alternative hypothesis; the mean price of fuel in in all petrol stations is more than 115 Australian Cents is
taken to be true. (Repetti, Roe & Gregory, 2015).
Section (3a): Give numerical summary and appropriate
graphical display for comparing the price of petrol of
those four major Brands
Descriptive statistics and a pie chart was uses to compare the price of petrol in four major brands.

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Caltex
Caltex
Woolworth
Coles
Express 7-Eleven
Mean
124.343
1 124.0504348
126.882828
3
121.182
5
Standard Error
0.66158
1 1.259930727
1.36678736
1
0.89985
4
Median 124.9 124.9 126.4 121.45
Mode 129.9 129.9 137.9 101.9
Standard Deviation
12.3770
4 13.5112518
13.5993625
3
12.9153
4
Sample Variance
153.191
2 182.5539252
184.942661
3
166.805
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Kurtosis -0.45402 2.58064847 -0.62151103 -0.84042
Skewness -0.1186 0.59472584
-
0.12153179
1
0.14979
1
Range 71 85.7 53 48
Minimum 78.9 99.9 99.9 99.9
Maximum 149.9 185.6 152.9 147.9
Sum 43520.1 14265.8 12561.4 24963.6
Count 350 115 99 206
From the descriptive data analysis it the mean price of fuel was 124.3, 124.1, 126.9 and 121.2
for Caltex, Caltex Woolworths Coles Express and Seven Eleven respectively. The count or number of
petrol station were 350, 115, 99 and 206 for Caltex, Caltex Woolworths Cole Express and 7-Eleven
respectively.
Chart Title
caltex caltex woolworth Coles Express 7-Eleven
Caltex and 7-Eleven were had the most petrol stations compared to the other two brands;
Caltex Woolworths and Coles Express. It is apparent the 7-elevenn had the least mean price of fuel

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which may be a major contributor to the large share market. (Tanford, Baloglu & Erdem, 2012). Again
Caltex has the minimum among the minimum fuel prices among the four groups and thus had the most
market share. It is also noteworthy that the two leading brands fuel prices had the least standard
deviation compared to the two other brands (Foster, Meijer, Schuh, & Zabek, 2011)
Section (3b): Perform a suitable hypothesis test at a 5%
level of significance to test whether there a price
difference among these four major Brands
A hypothesis was formulated and ANOVA was used to test the truth value of the assertion.
Analysis was conducted using Excel analytics.
H0: The mean fuel prices mean across all groups was equal
H1: The mean fuel prices in at least one of the major brands is not equal.
ANOVA
Source of
Variation SS df MS F P-value F crit
Between Groups 2462.39 3 820.7967 4.96649 0.002028 2.616528
Within Groups 126594.5 766 165.267
Total 129056.9 769
At 95% level of confidence was used and the tabulated p-value was 0.05. From the ANOVA test the p-
value was 0.002 thus the null hypothesis not accepted and therefore alternative assertion; the mean
fuel prices in at least one of the major brands is not equal, is taken to be true. The result signifie there is
significant price difference among the four brands. From the analysis it is apparent that 7-Eleven has the
lowest mean fuel prices at 121.1825 Australian cents. (Sallee, West & Fan, 2016).
Section 4: Sample survey at KOI University
The data obtained from the sample were analyzed and the results were as follows
Mean 3.285714
Standard Error 1.084837
Median 2
Mode 1
Standard Deviation 2.870208
Sample Variance 8.238095
Kurtosis 2.40403
Skewness 1.613144
Range 8
Minimum 1

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Maximum 9
Sum 23
Count 7
Chart Title
7-Eleven Budget caltex BP
Metro Fuel Independent Coles Express caltex woolworth
7, 1, 9 ,2 ,2 ,1 , 3and 5 out of the 30 sampled students KOI university used 7-Elven, Budget,
Caltex, BP , Metro fuel, Independent , Coles Express and Caltex Woolworths fuel suppliers respectively.
The most preferred fuel service provider was Caltex with 9 students followed closely by 7-Elven with 7
students, while the least preferred was Budget and Independent both having 1 student.
Conclusion
Form the above discussion it is apparent that fuel prices have a significant relationship with the
choice the consumers’ decision on fuel service providers. From the research, it is also ostensible that
there is a significant difference in the price of fuel across different fuel service provides. Since price is a
significantly influences consumers choice, the brand that sell at prices such as Caltex and 7-Eleven have
a competitive edge against other brands selling at higher prices. This brands therefore own a high
percentage of market share as depicted by the data analysis results. Another shared relationship by
brands with a high market shared is price fluctuation. The top brand have small standard deviation
compared to the other brands. The statistics infer that the consumer choice of service provider is
influence also by the fluctuation aspect of price such that consumers prefer service providers with more
consistent prices. As discussed above price is a big determiner of consumers’ choice, however there are
very few research done on the subject, more research is need to examined the theory on other
geographical area.

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