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:

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

Where:

• (n = 10) (the number of employees)
• (\sum{x} = 773) (the sum of the interview test scores)
• (\sum{y} = 724) (the sum of the performance scores)
• (\sum{xy} = 56676) (the sum of the products of x and y)
• (\sum{x^2} = 60475) (the sum of the squares of x)
• (\sum{y^2} = 53212) (the sum of the squares of y)

Substituting these values into the formula:

$r = \frac{10(56676) - (773)(724)}{\sqrt{(10 \times 60475 - 773^2)(10 \times 53212 - 724^2)}}$

Calculating:

1. Calculate the numerator: $10(56676) - (773)(724) = 566760 - 559012 = 7748$
2. Calculate the first part of the denominator: $10 \times 60475 - 773^2 = 604750 - 597529 = 8221$
3. Calculate the second part of the denominator: $10 \times 53212 - 724^2 = 532120 - 524176 = 7944$
4. Combine: $\sqrt{8221 \times 7944}$

Calculating this gives approximately (\sqrt{65273484} \approx 8081.79).

Thus, the denominator becomes:

$\sqrt{8221 \times 7944} \approx 8081.79$

Now substitute back into the formula:

$r \approx \frac{7748}{8081.79} \approx 0.96$

Therefore, the product moment correlation coefficient is approximately 0.96.