A chemical engineer is testing the carbon dioxide emissions of 11 prototype hybrid engines. The emissions, yyy grams per kilometre, for a random sample of 11 engines were recorded as follows:
175,45,95,42,65,60,15,80,48,72,56175, 45, 95, 42, 65, 60, 15, 80, 48, 72, 56175,45,95,42,65,60,15,80,48,72,56
Determine the median and the lower and upper quartiles for these data.
An outlier is defined as any value that is more than 1.5×interquartile range1.5 \times \text{interquartile range}1.5×interquartile range above the upper quartile or below the lower quartile.
Show that 175 is the only outlier in this dataset.
On a scale from 0 to 200, draw a box plot for these data, clearly indicating the outlier.
The engineer decides to omit the value 175 from the sample as it represents an engine failure.
Show that for the remaining 10 engines, Syy=4479.6S_{yy} = 4479.6Syy=4479.6.
The engineer also recorded the mass of each of these 10 engines, xxx kg. For this reduced sample, it is given that Sxx=5200.5S_{xx} = 5200.5Sxx=5200.5 and Sxy=−112.4S_{xy} = -112.4Sxy=−112.4.
Calculate the product moment correlation coefficient (r) between the engine mass and the carbon dioxide emissions for these 10 engines.
An analyst claims that heavier hybrid engines tend to produce significantly higher carbon dioxide emissions. Comment on this claim using your result from part (e).
Practise Edexcel A Level Maths Regression, Correlation and Hypothesis Testing with exam-style questions for A Level Maths. 100 questions covering Exponential Models, Measuring Correlation, and Hypothesis Testing for Zero Correlation, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.