# MAT10251 STATISTICAL ANALYSIS

**Data Analysis Project – Part B**

**Due: ** Week 8 Sunday 13 January 2019

**Value: ** 15%

**Objectives:** 1 to 5

**Topics:** 1, 5 and 6

**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.

**Part B Submission**

You should submit one word document consisting of

· Part B coversheets – first four pages, including completed self-marking sheet for Part A with reflection.

· Copy of your Part A submission.

· Written answers for Part B as components of a report – this should follow the format given on page 5 of Part B coversheets

· Appendices for Part B, which contain full statistical working for the required statistical tasks.

**Part B Preparation**

While the submission date for Part B is Sunday 13 January 2019, you should be working on Part B during Weeks 5 to 8.

It is recommended that you follow the following timetable

· Self-marking of, and reflection on, Part A should be completed in Week 5

· Question 1, covering Topic 5, should be completed in Week 6

· Question 2, covering Topic 6, should be completed in Week 8

**Tasks**

**Task 1** ** Part A Self-Marking – 5 marks**

**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 (19 marks)**

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 (9 marks)**.

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 (10 marks)**

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?

**Notes:**

· You may need to transform or manipulate your sample data, before using Excel for the required statistical calculations.

· Use Excel for statistical calculations. You do not need to repeat any Excel calculations by hand. However, make sure that you define your random variables and include any steps not given by Excel. For example, in a hypothesis test include the null and alternative hypotheses, along with the decision to reject or not reject the null hypothesis.

· Mention any assumptions you need to make.

· Comment on why the test or confidence interval has been chosen

· Make sure you interpret confidence intervals and write a conclusion to hypothesis tests.

**Task 3 – Part B Written Task – Components of a report (6 marks)**

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.

**Marking Criteria – Part B**

**Read these marking criteria carefully and consider them when preparing Part B.**

See the marking and feedback sheet, page 4 of Part B coversheets, for allocation of marks.

**Part A Self-Marking**

Full marks will be given for an *“acceptable self-marking and reflection”*. This is defined as the majority of errors (in particular major or obvious errors) are recognised and considered in marking and reflection.

Zero or partial marks will be given if:

· no or minimal reflection

· no self-marking

· major errors are not recognised.

**Statistical Calculation**

· For the** intervals and tests** marks will be given for:

- Choice of appropriate statistical technique/s.
- Random variables defined.
- Correct hypotheses for a test.
- Correct Excel output.
- Correct interpretation of results.

**Written Task – Components of a longer report**

· 200 to 400 words and one to three pages – marks will be deducted if this is greatly exceeded.

· To obtain full marks must:

- Be well structured and analysed
- Answer the questions and clearly communicate the results of the Excel output in language appropriate for your audience.
- Include an introduction to and conclusion for each question.
- Include appropriate Excel output
- For each question the following rubric will be used

Mark

Poor

0

Question not introduced and/or results not presented.

Confused response. Incorrect and/or inconsistent comments and conclusions.

Unnecessary statistical jargon, especially symbols, equations and definitions (copied from the textbook)

Question unanswered.

Acceptable

1

Question introduced and results presented.

Minimal interpretation and/or conclusions on how to use the information and/or only minimally relates information obtained to fuel price.

Only minor errors and inconsistencies in comments and conclusions.

Question answered.

More than acceptable

2

Results presented and question introduced and answered, clearly and concisely.

Includes interpretation and/or conclusions on how to use the information and/or relates information obtained to fuel price.

No errors and inconsistencies in comments and conclusions.

Question answered with justification

· For each major spelling and/or grammatical error half a mark will be deducted, up to a maximum of two marks.

· Also up to two marks may be deducted for poor structure and presentation.

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