MAT10251 Statistical Analysis Data Analysis Project Part C

MAT10251 STATISTICAL ANALYSIS
Data Analysis Project – Part C
Please Include Part C Coversheet
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Question 1: Statistical Inference Topic 7
Oz-Fuel-Watch wished to know if, on 1st August 2018, the mean the price of Diesel was less
in the capital city Brisbane, or elsewhere in the regional states.
Data was obtained from the petrol pumps in Queensland, both from regional and capital-
Brisbane areas in a random sample of 80 pumps. The sample consisted of 38 petrol pumps
from regional areas and 42 pumps from capital- Brisbane.
The boxplot below showed that the price of Diesel in Regional cities as well as in Capital-
Brisbane on 1st August 2018. It can be easily noted that median of Diesel the prices in
regional cities was greater than that of the price in the capital city, Brisbane. A positive
skewness was identified from the spread of the two side-by-side boxplots.
Diesel_BrisbaneDiesel_Regional
160
155
150
145
140
Diesel Prices (Cents per liter)
139.9
Box Plots for Diesel Prices in two regions of Queensland
Figure 1: Side-by-side Box Plot for Diesel The prices
The apparent difference in the price of Diesel in Regional as well as in Capital-Brisbane on
1st August 2018 is significant or due to sampling error was tested using a Z-test and the
following table illustrates the results.
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Table 1: Z Test for Differences in Two Means
From the p-value, the probability that there was any difference in Diesel the prices between
the regional cities and the capital city Brisbane was 0.18. That is a realistic and likely event.
Hence, the sample provides no evidence that there was an actual difference in the average the
prices of Diesel between regional cities and the capital city on 1st August 2018. So, motorists
who bought Diesel from either a regional or the capital city paid approximately same the
price for his or her fuel.
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Questions 2: Simple Linear Regression
Oz-Fuel-Watch was interested in exploring the relationship between Unleaded 91 and
Diesel the prices. Expecting that Diesel the price would influence Unleaded 91 the prices,
the Diesel the price was as the independent variable and the price of Unleaded 91 as the
independent variable to predict the price of Unleaded 91 based on Diesel the prices. A
positive relationship between the two fuels was expected on 1st August 2018.
The regression equation was evaluated as Pr ice Unleaded 91=0 .82∗Diesel Pr ice+ 18. 058 ,
where the correlation coefficient was 0.513 and the coefficient of determination was
evaluated to be 0.263.
As expected, the scatterplot shows that the price of Unleaded 91 was higher in cities,
where Diesel the prices were also comparatively higher than other places. However, while
this positive relationship was approximately linear it was also moderately strong. For one
cent the price increase in Diesel, then the price of Unleaded 91 was expected to increase
by 0.82 cents. Also, an initial price of 18.06 cents was identified for Unleaded 91, even if
the price of Diesel becomes zero. Therefore Unleaded 91 was expected to cost 18.06
cents even if Diesel became free in the market.
Figure 2: Scatter Plot for the prices of Unleaded 91 fuel on the prices of Diesel
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