Statistical Analysis Subject

Written Answer Part B Components of a longer report

The questions in part B both deal with the question of whether or not motorists view the price of the fuel as expensive though from different perspectives.

Question 1 in particular answers the question of whether the price of the fuel is expensive from the perspective of the population mean. The sample mean was estimated to be 145.3375 cents.

The results are as follows:

The interval was found to be [143.7074 , 146.9709] cents

Since the interval does not include the value $1.50 or 150 cents, the null hypothesis is rejected. Comment by Badri Bhattarai: ????? please display your excel output.

Question 2 on the other hand answers the question of whether or not the fuel price is expensive from the perspective of a subset (more than 25% of petrol stations) of the sample having the fuel price at least $1.50 per litre.

Calculations were done and the results are as follows:

It was found that the price of fuel in 24 out of 80 petrol stations in the state was higher than $1.50. This translates to 30%.

B.1 Average Price Unleaded 91/Diesel Price

No, the average price of fuel on that day and in the state specified was not expensive. This is so since as per the interval test in statistics that was carried out (check appendix), the null hypothesis which states that the fuel was expensive was rejected in our case.

B.2 Unleaded 91/Diesel Price Expensive

Yes, the price of fuel was at least $1.50 per litre in more than 25% of petrol stations in the state specified by the sample.

From the foregoing, we conclude that using the criteria where motorists perceive fuel price to be expensive when the price of fuel is at least $1.50 at more than 25% petrol stations in a state, the price of the fuel was expensive on the day in the state specified. Comment by Badri Bhattarai: Support your answers with your excel outputs

Appendices Part B

Appendix B.1 – Statistical answer for Question 1

The random variables were defined as follows:

· X_ is a random variable representing the sample mean.

· Sigma represents the standard deviation of the data from the mean.

· N represents the number of entries or petrol stations in the sample.

The following assumptions were made in the calculation and inference of the data:

X ~ N(X_ , Sigma2) i.e. X follows a normal distribution with mean= X_ and variance Sigma2.

The interval test was chosen in this case. This is because with the descriptive statistics that were previously calculated it was easier and faster to use the interval method. Also, the interval method does not require much calculation in the event that the average for which the price of fuel has to be to be considered expensive changes from $1.50. in fact, all that will be needed is to check whether the new average falls in the interval or not and make a decision.

Hypothesis testing

Null hypothesis: The price of fuel is expensive. In other words, the average price is at least $1.50.

Alternative hypothesis: The price of fuel is not expensive. In other words, the average price is less than $1.50.

To test the above hypothesis, a confidence interval was constructed as shown below:

X_ ± sigma/ where X_= 145.3375 cents, sigma= 7.4538 and N=80

The 95% confidence interval was found to be [143.7074, 146.9709] cents.

When comparing the value 150 cents to the interval, it can be seen that the value falls outside the interval on the upper limit. Therefore, the null hypothesis is rejected.

For question 1, the excel output used was that of the descriptive statistics that are needed in the calculation of the interval.

Interpretation of results: since we have failed to reject the null hypothesis, we conclude that the price of fuel is not expensive as per the criterion used in question 1.

Appendix B.2 – Statistical answer for Question 2

For question two, only one random variable was defined. X represents the individual price of fuel at each petrol station in the state.

The following logical function was used in excel: =IF(C2:C81>150,1,0) where the column C contained the price of fuel at each petrol station in cents. The column created by this logical function was then summed to find out the total number of stations which had at least a fuel price of 150 cents.

Hypothesis testing

Null hypothesis: the percentage of petrol stations with fuel price higher than 250 cents is greater than 25% hence fuel price is expensive.

Alternative hypothesis: the percentage of petrol stations with fuel price less than 250 cents is less than 25% hence fuel price is not expensive. Comment by Badri Bhattarai: ???

Interpretation of results: since we have failed to reject the null hypothesis, we conclude that the price of fuel is expensive as per the criterion used in question 2. The excel output is as shown below:

Do not cut my marks as I have been approved by my unit assessor because I have got the extension but I can’t be able to upload my assignment again thill the extension date so she reset my link. The attached copy of email you can see below thanks.

2

Sheet1

	Max Marks	Recommended Marks
Cover sheet or sample incorrect	-2.0
Format incorrect, including name	-2.0
Statistical Calculations
Graph (Frequency Histogram or Polygon)	4.0	4.0
Descriptive Statistics	4.0	4.0
Total Descriptive Statistics	8.0	8.0
Written Answer (Component of a business report)
Introduction and data	2.0	0.0
Comments on graph	3.0	3.0		`
Comments on descriptive statistics	4.0	3.0
Difference in measures of central tendency	1.0	1.0
Structure, grammar and spelling	2.0	2.0
Total Report	12.0	9.0
Total	20.0	17.0

Sheet2

Sheet3

Max MarksMark

Cover sheet or sample incorrect-2

Format incorrect, including file name-2

Self-Marking and Reflection Part A (5 marks)

Self-Marking Part A22.0

Reflection32.0

Part B Statistical Inference Tasks (19 marks)

Statistical Inference Question 1

Choice of technique, assumptions & other required steps41.0

Calculation (Excel output)30.0

Conclusion20.0

Statistical Inference Question 2

Choice of technique, assumptions & other required steps50.0

Calculation (Excel output)30.0

Decision and conclusion20.0

Written task - Discussion and results (6 marks)

Question 121.0

Question 220.0

Structure, grammar and spelling21.0

Total Part B307.0

Sheet1

	Max Marks	Mark
Cover sheet or sample incorrect	-2
Format incorrect, including file name	-2
Self-Marking and Reflection Part A (5 marks)
Self-Marking Part A	2	2.0
Reflection	3	2.0
Part B Statistical Inference Tasks (19 marks)
Statistical Inference Question 1
Choice of technique, assumptions & other required steps	4	1.0
Calculation (Excel output)	3	0.0
Conclusion	2	0.0
Statistical Inference Question 2
Choice of technique, assumptions & other required steps	5	0.0
Calculation (Excel output)	3	0.0
Decision and conclusion	2	0.0
Written task - Discussion and results (6 marks)
Question 1	2	1.0
Question 2	2	0.0
Structure, grammar and spelling	2	1.0
Total Part B	30	7.0

Sheet2

Sheet3

Max MarksRecommended

Marks

Cover sheet or sample incorrect-2.0

Format incorrect, including name-2.0

Statistical Calculations

Graph (Frequency Histogram or Polygon)4.04.0

Descriptive Statistics4.04.0

Total Descriptive Statistics8.08.0

Written Answer (Component of a business

report)

Introduction and data2.00.0

Comments on graph3.03.0

Comments on descriptive statistics4.03.0

Difference in measures of central tendency1.01.0

Structure, grammar and spelling2.02.0

Total Report12.09.0

Total20.017.0