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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

Statistics Value

Sample Size

Mean

Standard Deviation

Minimum

Q1

Median

Q3

57670

140.054

13.315

65.9

130.900

139.500

148.900


Statistics and Data Analysis.jpg

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

T Test: One Sample















SUMMARY


Alpha

0.05




Count

Mean

Std Dev

Std Err

t

df

Cohen d

Effect r

57670

140.0537

13.31467

0.055444

451.874

57669

1.881665

0.883046

 

 

 

 

 

 

 

 

T TEST



Hyp Mean

115





p-value

t-crit

lower

upper

sig



One Tail

0

1.64488



yes



Two Tail

0

1.960005

139.9451

140.1624

yes



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.


7 - Eleven

Caltex

Caltex Woolworths

Coles Express

Mean

140.39

141.93

141.36

148.03

Standard Error

0.12

0.13

0.13

0.23

Median

139.95

141.4

141.35

146.9

Mode

147.9

139.9

139.9

139.9

Standard Deviation

12.65

13.40

13.04

12.97

Sample Variance

160.06

179.57

169.94

168.33

Kurtosis

2.75

4.38

3.89

0.01

Skewness

-0.49

-0.99

-0.88

-0.01

Range

95.1

105

99

86

Minimum

72.8

65.9

72.9

86.9

Maximum

167.9

170.9

171.9

172.9

Sum

1511407

1528063

1521867

473857

Count

10766

10766

10766

3201

Statistics and Data Analysis1.jpg

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

Groups

Count

Sum

Average

Variance



7 - Eleven

10766

1511407

140.387

160.0598



Caltex

12768

1811151

141.8508

173.3717



Caltex Woolworths

11849

1674538

141.3231

165.6719



Coles Express

3201

473857

148.0341

168.3281










ANOVA







Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

148622.2

3

49540.74

296.8746

1.5E-190

2.605139

Within Groups

6438011

38580

166.8743











Total

6586633

38583

 

 

 

 

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

Brand

Frequency

Percentage

7-Eleven

2

6.7%

BP

4

13.3%

Budget

1

3.3%

Caltex

5

16.7%

Caltex Woolworths

2

6.7%

Independent

4

13.3%

Metro Fuel

6

20.0%

Mobil

1

3.3%

Speedway

2

6.7%

United

3

10.0%

Total

30


Statistics and Data Analysis2.jpg

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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