2. A supermarket manager believes that those of her staff on lower rates of pay tend to work more hours of overtime.
- Suggest why this might be the case.
To investigate her theory the manager recorded the number of hours of overtime, \(h\), worked by each of the store's 18 full-time staff during one week. She also recorded each employee's hourly rate of pay, \(\pounds p\), and summarised her results as follows:
$$\Sigma p = 86 , \quad \Sigma h = 104.5 , \quad \Sigma p ^ { 2 } = 420.58 , \quad \Sigma h ^ { 2 } = 830.25 , \quad \Sigma p h = 487.3$$
- Calculate the product moment correlation coefficient for these data.
- Comment on the manager's hypothesis.