Analysis of Petrol Prices in Australia

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STATISTICS AND DATA ANALYSIS
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1. Section 1: Introduction
a. Statistical modelling is an approach in data analysis that assist researchers discover certain
information regarding a phenomenon that is assumed to be in existence. Through modelling
of statistics, one is capable of identifying trends and analysing variability that exist in a data
set (Friendly & Meyer, 2016). Modelling in statistics is a unifying strategy that combines
both the estimation and hypothesis testing. Estimation allows for generalization of certain
findings from a sample data to the entire population on the other hand hypothesis testing is
applied to determine the complexity of the statistical model. Statistical modelling does assist
in prediction. Prediction entails evaluating how changes in a particular data set affect the
output of another. In addition to the prediction, modelling also allows a researcher to
provide explanations on the relationship between variables.
In this report the aim is to analyse the service station history prices so as to support the
activities of the NRMA. NRMA is an agency that is responsible for giving media reports to the
public with regard to current trends in the petrol prices (Kroese & Chan, 2014). For the
agency to provide relevant and accurate information, there is need for the historic data to
be analysed and trends evaluated. Microsoft excel will be applied in breaking down the past
data sets and conclusions drawn.
b. Dataset 1
The data set 1 is a subset of service station and price history data that is availed by the
government of Australia. Petroleum is one of the products that is massively consumed by
the Australians, for this reason the government has the responsibility of controlling its
supply so as to ensure the activities in the economy are not disrupted by shortages. One of
the ways of influencing the petroleum service industry is by providing the citizens of the
nation with periodic information regarding the occurrences taking place in the industry. By
definition secondary data is data that has been collected by someone other than the current
user. The data set 1 having been collected by the Australian government is treated as
secondary data. Some of the variables involved in the data are price of petrol and brand of
service station. To collect the data, the government might have applied questionaries to
interview the public or just used past records stored by some of the largest stakeholders in
the industry.
c. Dataset 2
Dataset 2 was collected from a sample of 50 KOI students. The data having been collected
by the person undertaking the research is treated as primary data. The research is meant for
analysing the trends in the Australian petrol industry, it was thus not possible to raise the
necessary capital to collect adequate data to meet the right sample size requirements.
Another limitation of the study is that the sample space was restricted to students and
hence the research failed to take into account the views of other citizens of the nation. The
variable in the dataset was service stations in Australia
2. Section 2: Analysis of single variable in Dataset 1
a. The table below gives a summary of the distribution of the petrol prices in Australia.

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Price
Mean 123.06
Standard Error 0.43
Median 123.4
Mode 127.9
Standard Deviation 13.46
Sample Variance 181.11
Kurtosis 2.14
Skewness -0.55
Range 99.6
Minimum 55.9
Maximum 155.5
Sum 123057.8
Count 1000
Largest(1) 155.5
Smallest(1) 55.9
The mean price is 123.06 with the mode being 127.9 and median 123.4. All the three
measures of central tendency are close values which indicates that the data is less skewed.
The standard deviation is 13.46. The skewness of just -0.5 shows that only a few of the
variables do fall below the mean.
The figure below is a histogram of the data set.
The histogram is bimodal and bell shaped which can be interpreted as the data is normally
distributed, the lognormal distributed can best be applied in describing the distribution of
the data
b. Hypothesis testing
Hypothesis testing involves 5 general steps the first one is stating the null and alternative
hypothesis.
H0 : μ=115
H1 : μ> 115