MAT10251 Statistical Analysis Project: Fuel Price Analysis in NSW

This project involves a statistical analysis of fuel price data, focusing on Unleaded 91 prices in New South Wales. The analysis includes calculating confidence intervals to estimate the population mean price and conducting hypothesis tests to determine if motorists perceive the fuel prices as expensive. The project utilizes descriptive statistics and statistical inference techniques, such as confidence interval computation and hypothesis testing for a single proportion. The student reflects on the task completion process, highlighting areas of improvement for future assignments. The analysis concludes that based on the sample data, motorists would likely not perceive Unleaded 91 prices as expensive on July 31, 2018, in NSW.

Task 1
In case of Part A, the positive aspect was that the task could fulfil the desired
objectives by adhering to the instructions in relation to both report writing and also task
submission besides choosing the correct sample and product based on the student ID and
family name. The use of descriptive statistics techniques was also accurate and relevant to the
task at hand. However, an area of improvement pertains to the time taken for completion of
the task which happened owing to failure to refer to the textbook and the notes taken in the
class. The net result was that there was need to improve on the initial draft a number of times
which resulted in wastage of time and also resulted in unnecessary confusion. In order to
improve the situation, for future tasks I would refer to the relevant extract of text book and
class notes to avoid confusion and save time. The self-marking enabled me to evaluate my
work considering the marking rubric and the key requirements to be fulfilled. This exercise in
the future would enable me to ensure that the assignment I am about to submit fulfils all the
necessary parameters and lead to improvement in quality of my assignment.

Task 3: PART B Written Report
The key aim is to indicate the average Unleaded 91 price for New South Wales on
July 31, 2018. The computation of confidence interval is required to be carried out so as to
highlight the interval in which the population mean of Unleaded 91 price may be expected.
The necessary computations for determination of 95% confidence interval in this
regards is highlighted as follows.
The computation carried out above suggests with 95% confidence that the mean
population unleaded 91 price on July 31, 2018 for NSW is expected to lie within the interval
(141.55, 145.47) cents per litre. Further, a 5% chance does exist whereby the average
Unleaded price for the population may lie outside the above interval.
Based on past research, it has come to light that even if 25% of the petrol stations
located in the given states sell Unleaded 91 for not lower than 150 cents per litre, the
motorists tend to perceive the price as expensive even if the average price is lower than 150
cents per litre.
In order to ascertain if the motorists on July 31, 2018 perceived the Unleaded 91 to be
expensive in NSW, the hypothesis test needs to be conducted so as to check if the petrol
station population proportion selling fuel for not lower than 150 cents per litre is greater than
25% or not. The relevant output is illustrated as follows.

Taking the p value into consideration, it is appropriate to conclude that the proportion
of petrol stations in NSW on July 31, 2018 which sell Unleaded 91 for not less than 150 cents
per litre are less than 25%. Hence, the motorists would not perceive the price as expensive.

Task 2: Appendix
Question 1
Confidence interval of single mean is the correct technique to be deployed.
Confidence interval chosen = 95%
Despite the standard deviation of the population being unknown, Z statistics is
deployed. This choice may be justified on account of Central Limit Theorem as the sample
size of 80 is quite large in comparison to the minimum value of 30 highlighting that it would
be appropriate to term the given distribution as normal. Thee 95% confidence interval
computation including all intermediate calculations is highlighted as follows.
It is appropriate to conclude with 95% confidence that the mean population unleaded
91 price on July 31, 2018 for NSW is expected to lie within the interval (141.55, 145.47)
cents per litre.

Question 2
The hypothesis test for a single proportion is the relevant technique to be deployed.
The definition of the variables is given as below.
Sample proportion (p) = 21/80 = 0.2625 or 26.25%
The relevant hypotheses are indicated as follows.
H0: π ≤ 25% i.e. petrol retailers in NSW selling Unleaded 91 at price of atleast 150 cents per
litre on July 31, 2018 do not exceed 25%
H1: π > 25% i.e. petrol retailers in NSW selling Unleaded 91 at price of atleast 150 cents per
litre on July 31, 2018 do exceed 25%
The level of significance has been taken as 5%.
The underlying distribution can be taken as normal considering the fact that the sample size is
quite large and nπ and n(1- π) both exceed 5. As a result, the relevant test statistics would be
Z and the excel output of the hypothesis test is shown as follows.

Based on the p value approach, p value (0.60) > level of significance (0.05). Hence, the null
hypothesis is not rejected and alternative hypothesis is not accepted. Thus, it is appropriate to
conclude that petrol retailers in NSW selling Unleaded 91 at price of atleast 150 cents per
litre on July 31, 2018 were at most 25%. Thus, the motorists would not have perceived the
Unleaded 91 price as expensive on July 31, 2018 in NSW.