2 A greengrocer sells bunches of 9 carrots at his Saturday market stall. Tom and Geri are two Statistics students who work on the stall. Each selects a bunch of carrots at random.
- At home, Tom measures the length, \(x\) centimetres, and the maximum diameter, \(y\) centimetres, of each carrot in his selected bunch with the following results.
| \(\boldsymbol { x }\) | 16.2 | 13.1 | 10.4 | 12.1 | 14.6 | 9.7 | 11.8 | 13.6 | 17.3 |
| \(\boldsymbol { y }\) | 4.2 | 3.9 | 4.7 | 3.3 | 3.7 | 2.4 | 3.1 | 3.5 | 2.7 |
- Calculate the value of the product moment correlation coefficient.
- Interpret your value in context.
- At her home, Geri measures the length, in centimetres, and the weight, in grams, of each carrot in her selected bunch and then obtains a value of - 0.986 for the product moment correlation coefficient.
Comment, with a reason, on the likely validity of Geri's value.