MAT10251 Statistical Analysis Project: Queensland Fuel Prices

This project analyzes fuel price data from Queensland, focusing on Unleaded 91 prices. It involves calculating a 95% confidence interval for the average fuel price on September 11, 2018, and conducting a hypothesis test to determine if motorists would consider the prices expensive. The analysis uses a sample of 80 petrol stations, employing both confidence interval estimation and hypothesis testing techniques to draw conclusions about the population mean and proportion. The project also discusses the choice of statistical techniques, justifying the use of the Z-test based on the Central Limit Theorem and sample size. The findings indicate that the average Unleaded 91 price lies within a specific range and that a significant proportion of petrol stations charge prices considered expensive by motorists. The project highlights the application of descriptive statistics, and the importance of adhering to the assignment requirements, and also reflects on the use of self-marking activities.

Task 1
For Part A, a relevant positive is that the submission is in line with the requirements
and achieves the stated objectives with regards to the use of descriptive statistics. The excel
sheet also involves the use of various excel functions that are appropriate for this task. The
only weakness in context of Part A is the failure to refer to the relevant class notes and
textbook. This actually resulted in frequent changes to the draft solution so as to ensure that
all the requirements are complied with. In the future, I would be more vigil in this regards so
as to avoid this unnecessary hassle. The self-marking activity also helped me in ensuring that
the assignment complied with the requirements and hence could potentially lead to improve
quality of my assignments in the future.

Task 3: PART B Written Report
The key objective is to highlight the mean Unleaded 91 fuel price on September 11,
2018 in Queensland. This requires confidence interval computation with regards to the above
variable so that estimate about the population can be made using the sample data.
The required calculation for 95% confidence interval is highlighted in the tabular
manner illustrated below.
The above table highlights that Unleaded 91 fuel price in Queensland state as on
September 11, 2018 lies in between 156.45 and 158.82 cents per litre. Considering that the
confidence level is 95% for the interval estimated above, hence there is a 5% likelihood of
average price not lying the interval estimated above.
Past research indicates that motorists tend to consider the fuel price expensive when at
a minimum one fourth of the petrol stations in the state sell the fuel for price of atleast 150
cents per litre. The average price is not relevant to these motorists.
Hypothesis test has been carried out for determining if the motorists in Queensland on
September 11, 2018 would consider the Unleaded 91 price to be expensive or not in wake of
the necessary condition highlighted above. The output for this testing is attached below.

Based on the above hypothesis test, it is correct to draw conclusion that motorists in
Queensland on September 11, 2018 would consider the Unleaded 91 fuel prices as expensive.
This is because more than one fourth of the petrol stations in the state would be charging
atleast 150 cents per litre.

Task 2: Appendix
Question 1
The correct statistical technique is to determine single mean confidence interval. The selected
confidence interval is 95%. The key variables are defined below.
In the given case, the population standard deviation for the Unleaded 91 price is not
given, but still the choice of test statistics is Z and not T. The justification of this can be
provided with the aid of Central Limit Theorem as the current sample size of 80 significantly
exceeds the minimum requirement of 30 and distribution can be assumed as normal. The
complete computation of the 95% confidence interval is summarised as follows.
The above table highlights that Unleaded 91 fuel price in Queensland state as on
September 11, 2018 lies in between 156.45 and 158.82 cents per litre. The chances of error in
the above conclusion is 5%.

Question 2
For the analysis of the claim, the appropriate statistical technique is single proportion
hypothesis test. The key variables are defined as shown below.
Sample proportion (p) = 69/80 = 0.8625 or 86.25%
The requisite hypotheses for conducting hypothesis test are shown below.
Significance level = 5%
Considering the sample size as 80 and π as 0.25, it is evident that the relevant assumptions to
approximate the given distribution as normal are fulfilled as nπ > 5 and n(1- π) >5. Hence the
test statistics of choice is Z with the hypothesis test output highlighted below.

The approach involving p value is used for hypothesis testing. As p value (0.00) <
significance level (0.05), hence reject H0 and accept H1. Hence, it is correct to draw
conclusion that motorists in Queensland on September 11, 2018 would consider the Unleaded
91 fuel prices as expensive.