2. A tennis coach believes that taller players are generally capable of hitting faster serves. To investigate this hypothesis he collects data on the 20 adult male players he coaches.
The height, \(h\), in metres and the speed of each player's fastest serve, \(v\), in miles per hour were recorded and summarised as follows:
$$\Sigma h = 36.22 , \quad \Sigma v = 2275 , \quad \Sigma h ^ { 2 } = 65.7396 , \quad \Sigma v ^ { 2 } = 259853 , \quad \Sigma h v = 4128.03 .$$
- Calculate the product moment correlation coefficient for these data.
- Comment on the coach's hypothesis.