The Association of Malawi Mechanics has commissioned a study to investigate the link between engine wear and mileage. The main focus of the study is to determine whether the mileage can be used to indicate the likely lifespan of the engine on a car that has been used before. The AMM has sourced 42 cars which have suffered severe accident damage to bodywork (the engines are undamaged by accident) in order to dismantle and examine the inner engine parts for wear.

The selection criterion was 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 and natural oils. The AMM also wants to investigate the claim that synthetic oils cause less engine wear than natural oils.

Tables 1a and 1b show the mileage and engine wear for each car. Engine wear is measured in units of 'Iron PPM'. An engine with engine wear measuring 100 Iron PPM will be so damaged and worn out that the engine is considered destroyed. No new cars were used at any point during the data collection.

Another important aim of the study was to investigate any link between engine wear and whether a car is likely to pass its annual roadworthiness test (MOT Test). Any car that fails its MOT test is declared un-roadworthy and must either be scrapped or repaired.

The AMM asked licensed mechanics to measure the engine wear of 2098 cars during their annual MOT Test and to note whether the car passed or failed its MOT Test. Engine wear was graded from 1 up to 4 (4 being very high engine wear). This data is shown in Table 2. Furthermore, the AMM also defined engine wear as either 'excessive' or 'low'.

In summary, the principal goals of this study are:

(i) To find out if mileage is a reliable measure of engine wear

(ii) To determine whether mileage and engine wear have the same kind of relationship for synthetic and naturally oiled cars

(iii) To investigate the association between engine wear and roadworthiness (MOT Passes)

One possible outcome is that the AMM decides to actively promote the use of a particular engine oil type (synthetic or natural).  In addition, the AMM may 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.

Instructions

The task required is to analyse and evaluate the data in this study. Maximum amount of information from the datasets should be extracted

Present the results and your conclusions in the form of a report so that the Director of the AMM will be well informed before making any policy changes. You must give your own recommendations for policy changes regarding the type of oil the AMM should endorse and any rules on mileage advertising for second hand cars.

Your report must

• describe the variables in the study, including any lurking variables

• present a full numerical and graphical summary of the data

• highlight any outliers and describe their effect on the results

• explain the results and state the conclusions using a clear and non-technical language

• Suggest a suitable experiment (or experiments) for a future research project. Discuss the factors, response variables, lurking variables and treatments in sufficient detail. Make sure that the experiment you recommend fully obeys the golden rules of experimental design.