Fuel Price Comparison in Western Australia: Statistical Analysis Reveals Insights

Running Head: Statistics
Statistical Analysis Project
Part C
Student’s Name
Institution Affiliation

Running Head: Statistics
Part C
This project responds to the questions about fuels prices in Western Australia. It compares
prices of unleaded fuel and diesel, within the capital towns and towns in other regionals. This has
been done by applying the knowledge of statistical inference, regression analysis and correlation.
The results are discussed below.
1. Price Comparison Capital City versus Elsewhere (regional) in State
This section responds to the hypothesis that the mean price of fuel in capital city is less than
elsewhere in Western Australia. To investigate this, data of fuel prices were subjected to z-test,
the mean regional price of unleaded fuel were compared with mean capital price of unleaded
fuels. Z-test were used as the sample size were large, greater than 30. The table below shows the
results of the test.
z-Test: Two Sample for Means at 95% significance level
Means
Regional Unleaded 91 (Cents
per Litre)
Capital Unleaded 91 (Cents per
Litre)
Mean 155.9846154 154.997561
Known Variance 42.2661 17.5342
Observations 39 41
Hypothesized Mean
Difference
0
z 0.802878834
P(Z<=z) one-tail 0.211022385
z Critical one-tail 1.644853627
P(Z<=z) two-tail 0.422044771
z Critical two-tail 1.959963985
Hypotheses:

Running Head: Statistics
Null hypothesis: Regional mean price-Capital mean price =0
Alternative hypothesis: Regional mean price-Capital mean price not equal to 0
Results Decision
Z-stat<Critical(two tail) Fail to reject null hypothesis
P-value(PZ<=z) two tail > 0.05 Fail to reject null hypothesis
From the result in the above table it’s clear that the mean price of unleaded fuel in capital city is
not less than the mean price in the regional level. The null hypothesis have been adopted as the
z-statistic (0.80) is less than the z- critical (1.96) and the p-value (0.42) is greater than 0.05.
2. Relationship between Unleaded 91 and Diesel
This section explores the relationship between the price of unleaded fuel and the price of diesel
in Western Australia. This is to investigate whether two variables have a linear or non-linear
correlation. To do this unleaded fuel prices were assumed independent variable ( x )while diesel
price were dependent variable ( y ). The investigation was done into stages. First is construction of
scatter plot to identify the relationship that exists between the variables from the pattern. Second
is doing the regression analysis of the data of prices to determine the correlation coefficient,
coefficient of determine, slope coefficient and intercept coefficient between the two variables.
2.1. Scatter plot
The following chart is a scatter plot of unleaded fuel prices against diesel prices.