Statistical Analysis of Three Gasoline Blends and Their MPG

Introduction and problem background

Crescent Oil has developed three new blends of gasoline – Blend X, Blend Y and Blend Z, and must decide which blend or blends to produce and distribute.  A study of the miles per gallon ratings of the three blends is being conducted to determine if the mean ratings are the same for the three blends.

Five automobiles- 1, 2 3, 4 and 5, have been tested using each of the three gasoline blends and the miles per gallon ratings are shown on the accompanying Excel spreadsheet.

Based on the sample data we would like to determine whether the different blends of gasoline, produce significant differences in the average mpg. We would like to use the methods we have learnt so far in 361A to see if our result is statically significant. (Statistical significance refers to a result that is not likely to occur randomly but rather is likely to be attributable to a specific cause – in this case the different gasoline blends and different cars.)

Carry out the following tests and make preliminary findings:

1.For the sample data, calculate the means and standard deviations for the mpg for each of the three blends of gasoline – Blend X, Blend Y and Blend Z.  

2.Draw three boxplots using Excel for mpg, one for each blend of gasoline.

3.Run three two sample t-tests between the different blends of gasoline i.e. compare the means of Blend X and Blend Y, then Blend X and Blend Z and finally Blend Y and Blend Z. Are they the same or are they different?

4.Armed with this information above determine whether or not your results show that the three different gasoline blends produce the same average mpg or not. Your answers should specifically site the information you re using to make your determination. 

5.Re-run parts 1 - 4 above but this time your focus is on the mpg of each car for the 5 cars (car 1 through car 5) not for the three gasoline blends.

Your report should have the following sections, arranged sequentially: 

1. Introduction and problem background 

2. Data description and the business questions to be answered  

3. Initial data exploration – descriptive statistics/graphs  

4. Analyses  

5. Interpretation of results, deficiencies in methods, final conclusions and recommendations for decision-making 

Submission: Your initial report must be uploaded on Titanium as a single Microsoft Word or a pdf file. No email submission will be accepted. If a student disregards this and uses email to submit, a zero is assigned for the report. Submitting a report is no guarantee for receiving any credit.

Proposal Part 1: 20 points maximum based on the rubric, to be converted to 2% points of your total score for the class. 

Proposal Part 1 grading: Using rubric criteria (see below).

For Phase 1, feedback to be provided based on these components: 

1.Adherence to the project guidelines: Check to see whether you have included all the deliverables and the document meets the guidelines for structure (sections) and formatting. 

2.Quality and presentation of the project background and initial analyses: Check to see if you have included a clear description of the background, business questions, and accurate descriptive statistics and graphs, as needed to obtain useful insights relevant to the business questions (with interpretation – just not the numbers/graphs). Provide guidance so that the next steps in the analysis could be completed successfully.

3.Quality and clarity of writing (including grammar and organization): Check for flow, organization, grammatical errors and typos. For writing guidance, refer to the Business Writer’s Handbook.

Introduction & Background: 

a)Purpose, business problem description;

b)Description of variables and outline of the statistical methods to be applied (descriptive statistics for Phase 1 and inferential methods for Phase 2) a) Purpose unclear and the problem description vague;

b) Description of variables and statistical methods incorrect or vague (as relevant to each Phase) a) Purpose included but the problem description lacks clarity;

b) Outline of variables and statistical methods adequate (1 error at most) but can be improved

a) Problem well-defined and covers the scope; 

b) Variable descriptions and statistical methods accurately and clearly outlined