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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.

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

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

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

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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