PM608 Statistical Analysis: Engine Oil
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PM608 Statistical Analysis: Engine Oil
1 Scenario
The Society of Motor Engineers (SAE) has commissioned some research to investigate the links between engine wear and mileage.
The SAE has sourced 42 cars which have suffered severe accident damage to bodywork (the engines are undamaged by accident) to dismantle and examine the inner engine parts for wear. The criteria used for the selection of cars for the study is that the cars must have an accurate record of all oil changes (service record) which also states the type of oils used in the engine.
There are two main types of engine oil:
· synthetic oils
· natural oils
The SAE wants to investigate the following:
· Determine whether the mileage can be used to indicate the likely life of the engine of a second-hand car.
· Synthetic oils cause less engine wear than natural oils.
· Certain oil types perform better in certain climates (warm or cold climates).
The data, presented in Tables 1a and 1b, includes
· the mileage of a car
· engine wear (measured in units of ‘Iron PPM’)
· the type of climate which the car was subject to.
An engine with engine wear measuring 100 Iron PPM will be so damaged and worn out that the engine is considered destroyed.
Your role in this is to use the data from tables 1a) and 1b) to help the SAE with its upcoming recommendations. They are considering the following:
· Actively promote the use of a particular engine oil type (synthetic or natural) in certain regions and certain climates.
· Introduce rules on advertising the condition of second-hand cars based on mileage.
However, these outcomes are only likely if the results are extremely significant. You may suggest other recommendations. The researcher reported that 1 or 2 of the measurements were taken before a fault was detected (and resolved) in the imaging processing. Your analysis must include all possible anomalies and state their possible impact on any conclusions.
Your task is to analyse and evaluate the data in this study and present the data and conclusions the form of a report so that the Director of the SAE will be well informed before making any policy changes. Furthermore, you must give your own recommendations for any policy changes regarding on the type of oil which the SAE should endorse and any rules on mileage advertising for second hand cars.
2 Assessment Approach
Any calculations must only use the methods and techniques described to you on this course.
The goal is to present your recommendations clearly so that the Director of the SAE can easily interpret your report. You MUST assume that the researcher and the Director of the SAE has no prior statistical knowledge, therefore care should be taken to fully explain the reasoning behind any analysis.
You should consider categorizing data in some new way that reveals patterns, and consider re-processing the data, perhaps creating a new variable or new tables. Clearly summarize any findings.
Microsoft Excel must be used for the statistical analysis you will perform below. Use of other software is not permitted.
The following must be completed below:
a) Quality Check
You must include a full numerical summary of the data, which includes:
· The 5-number summary.
· Measures of central tendency.
· Measures of variation.
· The skew and shape of the data.
You must include a critique and explanation of:
· the factors,
· treatments,
· any lurking variables,
which may be present in the study. You must highlight any possible errors in measurement, errors in experimental design, and any outliers. You must describe their effect on your conclusions.
b) Graphical Summary
You must produce two of the following graphical representation (must not pick more than 1 graphical representation) of the given data from the following options:
· Histogram
· Box Plot
· Modified Box Plot
· Cumulative Relative Frequency Curve
[For example, you may choose to have 2 boxplots, but any other graphical summaries after this will not be marked.]
Note: More sophisticated graphs will receive more marks.
c) Regression Analysis
You must produce:
I. two scatter plots
II. two least squares regression lines
III. two correlation coefficients, and
IV. two residual plots.
You must include:
V. comments on the validity of the regression model, using all the scatterplots, regression lines, correlation coefficients, and residual plots to do this.
VI. comments on how the collection method of the data and the quality of the data effects the validity of the models.
d) 2 Sample Confidence Interval
You must include:
I. How you are categorising the data and what 2-sample confidence interval you will use. That is:
· You must consider whether you are comparing tables 1a) and 1b) OR comparing data within either tables 1a) or 1b).
· Once you have decided, you must think about how you are going to compare the data sets.
· You must pick one of either difference of means or difference of proportions.
II. You must pick two confidence levels, stating clearly what confidence level you will use and why.
III. Full calculations must be included for each interval.
IV. A discussion on the physical interpretation of the two intervals
V. Comments on how the collection method of the data and the quality of the data effects the validity of the intervals.
End of scenario, the study data is below:
3 Data
Table 1a: Effect of Mileage on Engine Wear for Synthetic Oils
Mileage (1000s) |
Engine Wear (Iron PPM) |
Climate |
37.00 |
12.00 |
Warm |
78.00 |
39.00 |
Warm |
124.00 |
98.00 |
Warm |
119.00 |
58.00 |
Cold |
103.00 |
53.00 |
Cold |
21.00 |
10.00 |
Cold |
9.00 |
5.00 |
Cold |
27.00 |
11.00 |
Warm |
7.00 |
4.00 |
Cold |
42.00 |
10.00 |
Warm |
65.00 |
34.00 |
Warm |
41.00 |
31.00 |
Cold |
39.00 |
32.00 |
Cold |
16.00 |
11.00 |
Cold |
139.00 |
46.00 |
Cold |
55.00 |
34.00 |
Cold |
69.00 |
36.00 |
Cold |
51.00 |
14.00 |
Warm |
12.00 |
8.00 |
Cold |
29.00 |
9.00 |
Cold |
22.00 |
7.00 |
Warm |
Table 1b: Effect of Mileage on Engine Wear for Natural Oils
Mileage (1000s) |
Engine Wear (Iron PPM) |
Climate |
123 |
92 |
Cold |
62 |
66 |
Warm |
26 |
33 |
Warm |
29 |
37 |
Cold |
98 |
84 |
Cold |
110 |
98 |
Cold |
98 |
79 |
Cold |
32 |
35 |
Warm |
12 |
26 |
Warm |
4 |
28 |
Cold |
65 |
48 |
Warm |
29 |
33 |
Warm |
60 |
63 |
Cold |
18 |
20 |
Warm |
37 |
33 |
Warm |
67 |
61 |
Cold |
29 |
45 |
Warm |
81 |
77 |
Cold |
23 |
14 |
Warm |
78 |
70 |
Warm |
57 |
55 |
Cold |
2022-05-23