5. In a competition, a wine-enthusiast has to rank ten bottles of wine, \(A\) to \(J\), in order starting with the one he thinks is the most expensive. The table below shows his rankings and the actual order according to price.
| Rank | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Enthusiast | D | \(C\) | J | \(A\) | \(G\) | \(F\) | \(B\) | E | I | H |
| Price | A | \(C\) | D | \(H\) | \(J\) | B | \(F\) | I | \(G\) | \(E\) |
- Calculate Spearman's rank correlation coefficient for these data.
- Stating your hypotheses clearly, test at the \(5 \%\) level of significance whether or not there is evidence of positive correlation.
- Explain briefly how you would have been able to carry out the test if bottles \(B\) and \(F\) had the same price.