MAT10251 Project: Statistical Analysis of Fuel Price Data in Victoria

This assignment provides a statistical analysis of fuel price data from Victoria, focusing on diesel prices on July 17, 2018. It includes the computation of a 95% confidence interval to estimate the average diesel price, finding it to be between 151 and 153.15 cents per litre. The assignment further employs hypothesis testing to assess whether motorists considered diesel prices expensive, concluding that more than 25% of petrol stations were selling diesel at or above $1.5 per litre, thus supporting the claim. The statistical techniques used include confidence interval calculation and hypothesis testing of a proportion, with justifications for using normal distribution approximations based on the Central Limit Theorem and sample size. The analysis uses Excel for computations and deploys a p-value approach for hypothesis testing, leading to the rejection of the null hypothesis.

Task 1
In context of Part A, the substantial positive that has been realised is that the
submission managed to fulfil the various objectives that were stated in the assignment. Also,
the descriptive statistics usage was done correctly on the data provided with the use of
relevant functions in excel. An issue which I faced was that I had to frequently make
amendments in the initial draft as I made the mistake of not reviewing the class notes and
referred to the textbook. Going ahead, I would refer to these materials before beginning the
assignment so that time and resources are saved. Self-marking proved to be useful in
enhancing the overall quality of assignment and this could prove useful going forward also.

Task 3: Written Report
The primary aim is to indicate the average diesel price on July 17, 2018 in Victoria.
For this, the confidence interval needs to be computed which essentially provides estimate for
the population based on the sample data.
The computation of 95% confidence interval has been carried out using Excel with
the result pasted as follows.
The average price of diesel on July 17, 2018 in Victoria can be estimated to be lying
in the range of 151 cents per litre and 153.15 cents per litre. Further, there is a 5% likelihood
that the average diesel price would not lie in the above interval.
In accordance with past research, it is found that fuel price is considered expensive by
motorists when more than 25% of the petrol stations in Victoria tend to have a price of diesel
of a minimum of 150 cents per litre. The underlying technique for testing the given claim is
hypothesis testing whose output from excel is indicated as follows.

The above output highlights that the diesel price on July 17, 2018 would be
considered as expensive by the motorists as more than 25% of the petrol stations in Victoria
would sell the fuel at atleast $ 1.5 per litre.

Task 2: Appendix
Question 1
The confidence interval of a single variable is the requisite statistical test. Confidence interval
assumed is 95%. The variables used are outlined as follows.
The standard deviation of the population of diesel prices is unknown but owing to the
Central Limit Theorem, the given distribution is taken to be normal. This happens since the
sample size at 80 is significantly higher than the minimum requirement of 30. The 95%
confidence interval calculation with relevant intermediate steps is highlighted below.
The average price of diesel on July 17, 2018 in Victoria can be estimated to be lying
in the range of 151 cents per litre and 153.15 cents per litre. There is a 5% likelihood of the
above statement being false.
Question 2

The hypothesis testing of a proportion is the underlying statistical technique that would be
deployed. The definition of the main variables is offered as follows.
The hypotheses to be tested are illustrated as follows.
The assumed level of significance for this hypothesis test is 5%.
For the given data, sample size(n) is 80 with π being 0.25. Hence, nπ > 5 and n(1- π)
>5 because of which it would be appropriate to approximate the given distribution of diesel
prices as normal and deploy the test statistics as Z in the hypothesis testing. The output from
Excel is pasted below.

The p value approach is deployed for hypothesis testing in the above instance. The
computed p value is 0.00 and fails to exceed the level of significance which implies that null
hypothesis would be rejected in the favour of alternative hypothesis. Thus, motorists on July
17, 2018 in Victoria would have felt the diesel prices as expensive.