The following table records the age, aaa years, and the cumulative mileage, mmm thousand miles, for a sample of 8 used vehicles of the same model.
| Age (aaa) | 1.5 | 2.0 | 3.5 | 4.0 | 5.5 | 6.0 | 7.5 | 8.0 |
|---|---|---|---|---|---|---|---|---|
| Mileage (mmm) | 12 | 18 | 25 | 30 | 42 | 48 | 62 | 65 |
(You may use Saa=40.5S_{aa} = 40.5Saa=40.5 and Smm=2729.5S_{mm} = 2729.5Smm=2729.5)
Determine the exact value of ∑am\sum am∑am.
Find the value of SamS_{am}Sam.
Calculate the product moment correlation coefficient between aaa and mmm, giving your answer to 4 significant figures.
Interpret the value of the correlation coefficient in the context of the data.
A ninth vehicle is discovered. It is 8.5 years old and has a cumulative mileage of only 10 thousand miles.
Without further calculation, state whether the product moment correlation coefficient for the full set of nine vehicles will be higher, lower, or approximately the same as the value calculated in part (c). Give a reason for your answer.