3. The table below shows the population and the number of council employees for different towns and villages.
| Town or village | Population | Number of council employees |
| A | 211 | 10 |
| B | 356 | 2 |
| C | 1047 | 12 |
| D | 2463 | 21 |
| E | 4892 | 16 |
| F | 6479 | 25 |
| G | 6571 | 67 |
| H | 6573 | 45 |
| I | 9845 | 48 |
| \(J\) | 14784 | 34 |
- Find, to 3 decimal places, Spearman's rank correlation coefficient between the population and the number of council employees.
- Use your value of Spearman's rank correlation coefficient to test for evidence of a positive correlation between the population and the number of council employees. Use a \(2.5 \%\) significance level. State your hypotheses clearly.
It is suggested that a product moment correlation coefficient would be a more suitable calculation in this case. The product moment correlation coefficient for these data is 0.627 to 3 decimal places.
- Use the value of the product moment correlation coefficient to test for evidence of a positive correlation between the population and the number of council employees. Use a \(2.5 \%\) significance level.
- Interpret and comment on your results from part(b) and part(c).