The difference between new and old design tyres Wear-out distance

library(s20x)
distanceNew = with(tyredistance.df, DistanceNew)
distanceOld = with(tyredistance.df, DistanceOld)

boxplot(diffDistance, main = "Difference in the wear-out distance between new and old material tyre", ylab = "Wear-out distance (x1000 km)")

boxplot(diffDistance, main = "Difference between new and old design tyres Wear-out distance", ylab = "Wear-out distance (x1000 km)")

summaryStats(diffDistance)

Minimum value:           -33 
Maximum value:           54 
Mean value:              4.4 
Median:                  1.5 
Upper quartile:          17.25 
Lower quartile:          -6 
Variance:                465.83 
Standard deviation:      21.58 
Midspread (IQR):         23.25 
Skewness:                0.45 
Number of data values:   20 

Exploratory Analysis

Center: 4,400km

Spread: -33,000 - 54,000km

Skew: slightly right-skewed

normcheck(diffDistance)

Check the Normality of the whole model’s residuals by fitting a linear model. The model shows that the data has a slight right-skewed.

t.test(diffDistance)

    One Sample t-test

data:  diffDistance
t = 0.9117, df = 19, p-value = 0.3733
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -5.701217 14.501217
sample estimates:
mean of x 
      4.4 

Applying t test to compares the means of difference distance between new tyre and old tyre from the same car. p-value is greater than 0.05, which means that the difference in the wear-out distance between the new and old design is not statically significant.

Methods and Assumption Checks

We wish to find whether there is a difference in the wear-out distance between the new and old design tyre where the new and old tyre each was installed in the rear of the same car, so we carry out a paired-sample analysis.

Each tyre should be independent of the other. The Q-Q plot shows that the difference between the new tyre and the old tyre (new tyre distance - old tyre distance) is slightly right-skewed, but we can rely on the Central Limit Theorem to justify the Normality assumption.

The model fitted is \(\sf {diffDistance}_i = µ_{\sf diff} + ε_i\), where \(µ_{\sf diff}\) is the mean distance difference between new and old design tyre for each car, and \(ε_i\) \(_{\sim}^{iid} N(0, σ^2)\).

Executive Summary

We are interested in determining whether there is a difference between the average wear-out distance of a new design tyre and the average wear-out distance of an old design tyre where they were installed in the rear of the same car.

Our data involved two related measurements (on the wear-out distance of new and old design tyres), and the difference between the two wear-out distances has been analysed.

We observe that the difference in the wear-out distance between the new and old design is not statically significant. Therefore, this shows that the new design tyre does not have a better performance in terms of wear-out distance than the old design tyre.