Reference no: EM132216058

STATISTICAL ANALYSIS PROJECT -

This project leads you through a statistical analysis of fuel price data from an Australian state. This data was obtained from PetrolSpy Australia for a given day from a randomly selected sample of petrol stations in an Australian state with the price per litre of Unleaded 91 and Diesel recorded.

Part A covers parts of Topic 1, Part B parts of Topics 5 and 6 and Part C parts of Topics 7 to 9.

Project Situation -

Oz-Fuel-Watch regularly analyses fuel prices in various Australian states.

As a research assistant for Oz-Fuel-Watch, you are analysing the data for the day and state specified by your sample. For example, if your student ID number ends in 8 your sample is Sample 8. That is, you will be analysing fuel prices for New South Wales on 4 September 2018, using the sample data in columns AO to AR.

In each part of the project you are required to analyse your sample data in response to the given questions and provide a written answer. You can assume that the written answers are components of a longer report on fuel prices.

Project Preparation -

You are expected to use Excel when completing the project.

Your written answers presenting your findings and conclusions should be considered as a part of a larger report on Australian fuel prices. Each written answer should be a word document into which your Excel output has been copied

In addition, your statistical workings for Parts B and C should appear as appendices to your written answers. These should include all necessary steps and appropriate Excel output.

Each part of the project should be submitted as a SINGLE Word document, with appropriate Excel output added.

Notes

• You should not need to read beyond the study guide and textbook to complete the project.

Data Analysis Project - Part A

Purpose: To

• introduce you to the project data, situation and Excel
• use Excel to graph data and calculate summary statistics
• interpret and communicate Excel results.

Part A Question - Oz-Fuel-Watch has asked you to provide information on the price of either Unleaded 91 or Diesel on the day and in the state specified by your sample. In particular, information on the minimum and maximum price and the average price. Also required is an estimated price range for your given fuel.

Note:

• If your family name begins with A to M analyse Unleaded 91 prices.
• If your family name begins with N to Z analyse Diesel prices.

Data Analysis Project - Part B

Purpose: To

• obtain feedback on your submission in Part A and to gain experience in self-evaluation of submitted work
• apply your knowledge of statistical inference to answer questions about fuel prices by analysing the data and communicating the results.

Tasks -

Task 1 Part A Self-Marking -

When directed to do so during Week 5 complete the following tasks

1) Open your saved copy of your submission for Part A.

2) Replace the Part A coversheets (three pages) with the Part B coversheets (first four pages).

3) Rename and save this file as "Family Name_First Name_Part_B_Campus".

4) Use the solution template and marking guide provided to mark your submission for Part A. Enter recommended marks on the self-marking sheet for Part A, page 3 of the file in 3) above.

5) Write a short (approximately 200 words) reflection/feedback on your submission and marking of Part A. In particular:

• consider the good aspects of your submission, what did you do well
• identify where you made mistakes, and how you would avoid them in the future
• consider what you learnt from submitting and self-marking Part A.

This is to be entered in the space at the bottom of the self-marking sheet for Part A.

6) Save file. To be submitted with Part B - due Sunday 13 January 2019.

Task 2 Part B Appendix - Statistical Inference Tasks

The following statistical tasks should appear as appendices to your written answer. This should include all necessary steps and appropriate Excel output.

These appendices should come after your written answer within your single Word document for Part B.

Statistical Inference

Choose a level of confidence for the confidence interval in Question 1 and a level of significance for the hypothesis test in Question 2. Enter these values on page 2 of the Part B coversheets along with the sample number and fuel from Part A.

Question 1 and 2 Situation

Previous research undertaken by Oz-Fuel-Watch shows that motorists consider a fuel to be expensive if its price is $1.50 per litre or more. That is, at least $1.50.

Question 1 - Topic 5

Oz-Fuel-Watch has asked you whether motorists would consider the average price of your fuel expensive on the day and in the state specified by your sample.

To enable you to answer this question use Unleaded 91 (third column of your data) or Diesel (fourth column of your data) and an appropriate statistical inference technique to:

Estimate the population mean price of your fuel, Unleaded 91 or Diesel, on the day and in the state specified by your sample.

Question 2 - Topic 6

Past research shows that even when the average price is less than $1.50 per litre, motorists perceive fuel prices to be expensive when the price of a fuel is at least $1.50 at more than 25% of petrol stations in a state.

Oz-Fuel-Watch wishes to know if, using this criteria, the price of your fuel, Unleaded 91 or Diesel, was expensive on the day, and in the state, specified by your sample.

To enable you to provide this information use Unleaded 91 (third column of your data) or Diesel (fourth column of your data) and an appropriate statistical inference technique to answer the following question

On the specified day was the price of your fuel at least $1.50 per litre at more than 25% of petrol stations in the state specified by your sample?

Task 3 - Part B Written Task - Components of a report

For each question, present the results of your calculations, with your interpretation and conclusion as components of a longer report on fuel prices.

Use the instructions given on page five of the Part B coversheets.

This should be a one to three pages and 200 to 400 words.

It should be submitted as a Word file with Excel output included.

Make sure you:

• Introduce each question and put it in context.
• Answer the question in non-statistical language
• Present the results of your intervals or tests without unnecessary statistical jargon
• Include conclusions which answer the given questions.

Data Analysis Project - Part C

Purpose: To answer questions about fuel prices by applying your knowledge of statistical inference, and regression and correlation. To communicate the results.

Part C Preparation

While the submission date for Part C is Sunday 3 February 2019, you should be working on Part C during Weeks 9 to 11.

It is recommended that you follow the following timetable

• Question 1 covering Topic 7 should be attempted in Week 9
• Question 2 covering Topic 8 should be attempted in Week 10
• Question 3 covering Topic 9 should be attempted in Week 11

Task 1 Part C - Appendix Statistical Inference and Regression and Correlation Tasks

The following statistical tasks should appear as appendices to your written answer. This should include all necessary steps and appropriate Excel output.

These appendices should come after your written answer within your single Word document for Part C.

Question 1 Statistical Inference Topic 7

Capital city fuel prices are often less than elsewhere in the state.

Oz-Fuel-Watch wishes to know if on the day and in the state specified by your sample the mean price of your fuel, Unleaded 91 or Diesel, was less in the capital city than elsewhere in the state.

To enable you to provide this information use Location (second column of your data) and either Unleaded 91 (third column of your data) or Diesel (fourth column of your data) with an appropriate statistical inference technique to answer the following question

On the specified day was the mean price of your fuel less in the capital city than elsewhere in the state specified by your sample?

Questions 2 and 3 Simple and Multiple Linear Regression

Oz-Fuel-Watch is interested in exploring the relationship between Unleaded 91 and Diesel prices.

You are asked to construct a model of this relationship. To do this, first develop a simple linear regression model between Unleaded 91 and Diesel prices. Then develop a multiple linear regression model with location as a second independent variable. Finally choose and interpret the linear model that best fits your data.

Question 2 Simple Linear Regression Model Topic 8

To explore the relationship between Unleaded 91 and Diesel prices, use your fuel (Unleaded 91/Diesel) as the independent variable and the remaining fuel (Diesel/Unleaded 91) as the dependent variable.

Using this data develop and then explore a simple linear relationship between the two variables by:

• Plotting the data with a scatter plot.
• Calculating the least squares regression equation, correlation coefficient and coefficient of determination.
• Interpreting the gradient and vertical intercept of the simple linear regression equation.
• Interpreting the correlation coefficient and coefficient of determination. Are these values consistent with your scatter plot?

Question 3 Multiple Linear Regression Model Topic 9

To explore if location influences the relationship between Unleaded 91 and Diesel prices add Location (second column of your data) as a second independent variable to your simple linear regression model developed in Question 2.

Using this data develop and then explore the relationship between the three variables by:

• Calculating the multiple regression equation, multiple correlation coefficient, and coefficient of multiple determination.
• Interpreting the values of the multiple regression coefficients.
• Interpreting the values of the multiple correlation coefficient and coefficient of multiple determination. Compare these values with the corresponding values for the simple linear regression model.

Then determine the best model to predict the price of your dependent fuel by:

• Using appropriate tests to determine which independent variables make a significant contribution to the regression model.
• Using the results of the above tests to state the simple or multiple regression equation which best fits the data.

Task 2 - Written Answer - Components of a report

For Question 1 and Questions 2 and 3 combined present the results of your calculations, with your interpretation and conclusions as components of a longer report on fuel prices.

Use the instructions given on page four of the Part C coversheets.

This should be 300 to 700 words and three to six pages.

It should be submitted as a Word file with Excel output embedded.

Make sure you:

• Introduce each question and put it in context
• Answer the questions in non-statistical language.
• Present the result of your calculations and tests without unnecessary statistical jargon
• Include conclusions which answer the given questions.

In particular, for Question 2

• Include your scatter plot and discuss any apparent relationship between Unleaded 91 and Diesel prices. Comment on the strength, shape and sign of the relationship.
• Mention or explain your choice of independent and dependent variables

In particular, for Questions 2 and 3

• Include and justify the best model.
• Discuss and interpret the values of the regression and correlation coefficients of the best model.

Note - Please do part B & C.

Attachment:- Assignment Files.rar