Question

The "cold start ignition time" of an automobile engine is being investigated by a gasoline manufacturer. The following times (in seconds) were obtained for a test vehicle: 1.76, 1.84, 2.71, 2.26, 3.15, 3.21, 2.48, 1.87. A second formulation of the gasoline was tested in the same vehicle, with the following times (in seconds): 1.75, 2.08, 3.17, 3.21, 2.74, 2.83, 3.47, 2.47, 1.98, and 3.39. Use this new data along with the cold start times to construct comparative box plots.

Answer 1

The boxplots are on the figure attached. And the explanation is below.

Explanation:

For the first formulation we have the following dataset:

1.76, 1.84, 2.71, 2.26, 3.15, 3.21, 2.48, 1.87

We can construct a box plot with the following R code:

> x1<-c( 1.76, 1.84, 2.71, 2.26, 3.15, 3.21, 2.48, 1.87)

> boxplot(x1,main="Boxplot method 1")

For the scond formulation we have the following data:

1.75, 2.08, 3.17, 3.21, 2.74, 2.83, 3.47, 2.47, 1.98

And the boxplot can be constructed with the following R code:

> x2<-c(1.75, 2.08, 3.17, 3.21, 2.74, 2.83, 3.47, 2.47, 1.98)

> boxplot(x2,main="Boxplot method 2")

And we can get the comparative 5 number results for each case:

> summary(x1)

Min. 1st Qu. Median Mean 3rd Qu. Max.

1.760 1.863 2.370 2.410 2.820 3.210

> summary(x2)

Min. 1st Qu. Median Mean 3rd Qu. Max.

1.750 2.080 2.740 2.633 3.170 3.470

As we can see both histograms shows asymmetrical distributions. For the first method Mean>Median so then we can conclude that the distribution would be approximately skewed to the right. For the second case the Median>Mean so we can conclude that the distribution would be approximately skwewed to the left.