5 A psychologist investigates the relationship between 'openness' and 'creativity' in adults. Each member of a random sample of 15 adults is given two tests, one on openness and one on creativity. Each test has a maximum score of 75 . The results are given in the table.
| Adult | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O |
| Openness, \(x\) | 39 | 34 | 29 | 20 | 40 | 35 | 20 | 36 | 55 | 31 | 41 | 43 | 33 | 30 | 33 |
| Creativity, \(y\) | 59 | 34 | 17 | 29 | 49 | 46 | 45 | 54 | 60 | 38 | 46 | 35 | 43 | 56 | 34 |
\(n = 15 \quad \sum x = 519 \quad \sum y = 645 \quad \sum x ^ { 2 } = 19033 \quad \sum y ^ { 2 } = 29751 \quad \sum x y = 23034\)
- Use Pearson's product-moment correlation coefficient to test, at the \(5 \%\) significance level, whether there is positive association between openness and creativity.
- State what the value of Pearson's product-moment correlation coefficient shows about a scatter diagram illustrating the data.
- A student suggests that there is a way to obtain a more accurate measure of the correlation. Before carrying out the test it would be better to standardise the test scores so that they have the same mean and variance.
Explain whether you agree with this suggestion.