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BUS708 Statistics and Data Analysis - Kings Own Institute

Section 1: Introduction

a. Give a brief introduction about the assignment and search a related article and write a paragraph of summary which should be a support for your report.

The major objective of this study is to determine the factors that influence the price of the petrol in Australia. For the purpose of the study, the data was taken from the Australian Government Open Data and a total of 57670 records were collected for the statistical analysis. This data collection is an example of secondary data collection technique as the data was extracted from reliable Australian government source.

Give a short description about this dataset. Is this primary or secondary data?

b. Dataset 1
For the purpose of the study, the data was taken from the Australian Government Open Data and a total of 57670 records were collected for the statistical analysis. This data collection is an example of secondary data collection technique as the data was extracted from reliable Australian government source
Explain how you collect the data and discuss its limitation

c.Dataset 2
The second dataset is an example of primary data collection technique as the data is collected in the form of survey technique. A random sample of 30 KOI students were selected and the details regarding the petrol station they prefer to buy petrol was recorded and thus, it is an example of primary data collection technique

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Section 2: Analysis of single variable in Dataset

a. What is the shape of the distribution of the variable Price?

Summary Statistics

The descriptive statistics for the variable Price is given below

The mean price of the fuel is 140.054 ± 13.315 Australian cents with the recorded median fuel price is 139.5 Australian cents and the recorded minimum and maximum fuel price is 65.9 Australian cents and 179.9 Australian cents respectively. Going through the histogram, we see that the distribution of fuel price approximately has equal tail width on left and right side of the normal curve, indicating that the distribution of fuel price is normally distributed

b. Is the average price of petrol is in all service station in September 2016 is more than 115 Australian cents?

Here, we are interested in determining whether the mean petrol price differ significantly from 115 Australian cents we perform single mean z test

Null Hypothesis: H₀: µ = 115

That is, the mean petrol price do not differ significantly from 115 Australian cents

Alternate Hypothesis: H₁: µ > 115

That is, the mean petrol price is significantly more than 115 Australian cents

Level of Significance

Let the level of significance be α = 0.05

Here, the t test value is 451.874 and its corresponding p - value is 0.000 < 0.05, indicating that we need to reject the null hypothesis at 5% level of significance. Therefore, there is statistical evidence to say that the mean price of the petrol is more than 115 Australian cents
Conclusion
Here, the p - value of t test statistic is less than 0.05, indicating that there is statistical evidence to conclude that the mean price of the petrol is more than 115 Australian cents

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Section 3: Analysis of two variables in Dataset

Section 3:
Give numerical summary and appropriate graphical display for comparing the price of petrol of those four major Brands.
a.

Perform a suitable hypothesis test at a 5% level of significance to test whether there a price difference among these four major Brands.
b.
Here, we are interested in determining the mean petrol price differ significantly from 115 Australian cents we perform single mean z test
Null Hypothesis: H0: µ1 = µ2 = µ3 = µ4
That is, the mean petrol price do not differ significantly between Caltex, Caltex Woolworths, Coles Express and 7 - Eleven
Alternate Hypothesis: H1: µi ≠ µj
That is, the mean petrol price differ significantly between Caltex, Caltex Woolworths, Coles Express and 7 - Eleven
Level of Significance
Let the level of significance be α = 0.05

Anova: Single Factor

The value of f test value is 296.9 and its corresponding p - value is 0.000 < 0.05, indicating that we reject null hypothesis at 5% level of significance. Therefore, we say that the mean price of the petrol differ significantly between Caltex, Caltex Woolworths, Coles Express and 7 - Eleven

write an accurate information of the petrol price. Your answer should contain that whether there is price differences and if there is, try to find which Brand price is lowest.
c.
Conclusion
Here, the p - value of t test statistic is less than 0.05, indicating that there is statistical evidence to conclude that the mean petrol differ significantly between Caltex, Caltex Woolworths, Coles Express and 7 - Eleven

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Section 4: Collect and analysis Dataset

Section 4

a. Write an executive summary by combining all of your finding in the previous sections which must be a valuable for NRMA to report to media

The brand choice of the 30 randomly selected KOI students information is given below

About 20% of the KOI students prefer to use Metro Fuel brand, 16.7% of the students prefer to buy petrol in Caltex brand and 13.3% of the KOI students prefer to buy petrol in Independent shops

Discussion and conclusion

The major objective of this study is to determine the factors that influence the price of the petrol in Australia. For the purpose of the study, the data was taken from the Australian Government Open Data and a total of 57670 records were collected for the statistical analysis. This data collection is an example of secondary data collection technique as the data was extracted from reliable Australian government source

The mean price of the fuel is 140.054 ± 13.315 Australian cents with the recorded median fuel price is 139.5 Australian cents and the recorded minimum and maximum fuel price is 65.9 Australian cents and 179.9 Australian cents respectively. Going through the histogram, we see that the distribution of fuel price width was approximately equal on both left and right sides of the normal curve, indicating that the distribution of fuel price is normally distributed

Here, we are interested in determining whether the mean price of the petrol is more than 115 Australian cents, single mean z test was performed. The study findings say that the mean price of the petrol is more than 115 Australian cents. In order to determine whether there is a significant difference in the mean petrol prices among Caltex, Caltex Woolworths, Coles Express and 7 - Eleven brands, one way ANOVA was performed. The study findings suggest that there is statistical evidence to conclude that the mean price of the petrol differ significantly between Caltex, Caltex Woolworths, Coles Express and 7 - Eleven

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