A personnel manager wants to find out if a test carried out during an employee’s interview and a skills assessment at the end of basic training is a guide to performance after working for the company for one year - Edexcel - A-Level Maths Statistics - Question 1 - 2008 - Paper 1

To calculate the product moment correlation coefficient, we use the formula:

$r = \frac{n(\sum{xy}) - (\sum{x})(\sum{y})}{\sqrt{[n\sum{x^2} - (\sum{x})^2][n\sum{y^2} - (\sum{y})^2]}}$

Where:

• $n = 10$ (number of employees)
• $\sum{x} = 773$
• $\sum{y} = 724$
• $\sum{x^2} = 60475$
• $\sum{y^2} = 53122$
• $\sum{xy} = 56076$

Substituting the values:

$r = \frac{10(56076) - (773)(724)}{\sqrt{[10(60475) - (773)^2][10(53122) - (724)^2]}}$

Calculating each part:

1. $n\sum{xy} = 560760$
2. $(\sum{x})(\sum{y}) = 560612$
3. $n\sum{x^2} = 604750$
4. $(\sum{x})^2 = 597529$
5. $n\sum{y^2} = 531220$
6. $(\sum{y})^2 = 523776$

Now, substituting these values into the formula:

$r = \frac{560760 - 560612}{\sqrt{[604750 - 597529][531220 - 523776]}}$

Calculating:

$r = \frac{148}{\sqrt{[8221][7444]}}\approx 0.1553$

Thus, the product moment correlation coefficient r is approximately 0.155.