MAT10251 Statistical Analysis Project: Analyzing Fuel Price Data

This project involves a statistical analysis of fuel price data from an Australian state, focusing on Unleaded 91 prices. The analysis includes calculating a 95% confidence interval for the average Unleaded 91 price in Victoria on August 22, 2018, determining that the average price likely falls between 143.26 and 144.79 cents per litre. Additionally, a hypothesis test was conducted to assess whether the proportion of petrol stations selling Unleaded 91 at or above 150 cents per litre exceeds 25%. The results indicated that it does not, suggesting motorists likely did not perceive Unleaded 91 as expensive on that day. The project utilizes statistical techniques such as confidence intervals for a single mean and hypothesis testing for a single proportion, employing Z statistics based on the Central Limit Theorem due to the sample size. Excel outputs are used to support the hypothesis testing conclusions. The student also reflects on their learning process, emphasizing the importance of referencing class notes and textbooks for improved clarity and efficiency in completing assignments.

Task 1
With regards to Part A submission, the good things including being able to adhere to
the instructions and being able to fulfil the key objectives outlined. In this regards, the
various graphical representation and computation were completed in accordance with the
expectations. However, a key mistake which was made was lack of reference to the class
notes and textbook owing to which the amount of time taken to complete Part A was
considerably higher than expected. Also, in the initial drafts there was lack of understanding.
As a result, going forward, I would be proactive in referring to the book and class notes
before working on the respective assignments so that there is higher clarity. The self-marking
provided me with a chance of self-evaluate my own work and thereby highlights the extent to
which I feel that it meets the underlying requirements. Going forward, this would enable
improvement in my assignments as I need to make amendments in the submission till I feel
that during the self-evaluation, I deserve high grades.

Task 3: PART B Written Report
I was asked to highlight the mean Unleaded 91 price for Victoria on August 22, 2018.
In response to this question, computing the confidence interval would be required as it would
provide a range of values where the population mean of Unleaded 91 price would be
expected to lie.
The 95% confidence interval computation for the average Unleaded 91 price is
highlighted below.
From the above computation, it may be concluded with 95% confidence that the
average population unleaded 91 price on August 22, 2018 for Victoria would lie between
143.26 cents per litre and 144.79 cents per litre. It is noteworthy that there is a 5% chance
that the population average may not lie in the interval specified above.
Past research has indicated that even if 25% of state petrol stations tend to sell
Unleaded 91 at price of 150 cents per litre, then the same is perceived as expensive by the
motorists even though the average price may be lesser than 150 cents per litre.
Using the available sample data, a hypothesis testing has been conducted to test if the
proportion of petrol stations selling Unleaded 91 for atleast 150 cents per litre exceed 25% or
not. The relevant output of the hypothesis test has been obtained from Excel and attached
below.

From the p value, it can be concluded that the population petrol stations proportion
that sell Unleaded 91 for atleast 150 cents per litre do not exceed 25% and are significantly
less than the same. This implies that the motorists on August 22, 2018 would not have felt
that Unleaded 91 was expensive in Victoria.

Task 2: Appendix
Question 1
The relevant technique to be used is confidence interval of a single mean.
Confidence interval selected = 95%
Here X = Unleaded 91 price on August 22, 2018 at a sample petrol station located in Victoria
X- bar = Average Unleaded 91 price on August 22, 2018 at a sample petrol station located in
Victoria
μ = Average Unleaded 91 price for the population of petrol station located in Victoria on
August 22, 2018
Even though the population standard deviation is known, but still the Z statistics is used for
the estimation of confidence interval as the sample size is 80 which is significantly greater 30
and hence in line with the Central Limit Theorem, it would be appropriate to conclude that
the given distribution of Unleaded 91 prices are normally distribution. The computation of
the 95% interval with the intermediate calculations is exhibited below.
We can conclud with 95% confidence that the average population unleaded 91 price on
August 22, 2018 for Victoria would lie between 143.26 cents per litre and 144.79 cents per
litre

Question 2
The requisite technique to be used here is hypothesis test for a single proportion.
The relevant variables are defined below.
π = Population proportion of petrol retailers in Victoria selling Unleaded 91 at price of atleast
150 cents per litre on August 22, 2018
p = Sample proportion of petrol retailers in Victoria selling Unleaded 91 at price of atleast
150 cents per litre on August 22, 2018
Sample proportion (p) = 1/80 = 0.0125 or 1.25%
The requisite hypotheses are highlighted below.
H0: π > 25% i.e. petrol retailers in Victoria selling Unleaded 91 at price of atleast 150 cents
per litre on August 22, 2018 exceeded 25%
H1: π ≤ 25% i.e. petrol retailers in Victoria selling Unleaded 91 at price of atleast 150 cents
per litre on August 22, 2018 was at most 25%
The significance level has been assumed as 5%.
In the given case, the sample size is 80, owing to which nπ = 20 and n(1- π) = 60 which are
both greater than 5 and hence the given distribution can be considered as normal owing to
which Z statistics would be used for hypothesis test.
The excel output for a lower tail z test is given below.

The p value approach has been used to test the hypothesis. It is apparent that the p value is
lower than the assumed significance level of 0.05 and hence the available evidence is
sufficient to cause rejection of null hypothesis and acceptance of alternative hypothesis.
Hence, it may be concluded that petrol retailers in Victoria selling Unleaded 91 at price of
atleast 150 cents per litre on August 22, 2018 was at most 25%. Therefore, the motorists
would not have found the price of Unleaded 91 as expensive in Victoria on August 22, 2018.