- The ages, in years, of a random sample of 8 parrots are shown in the table below.
| Parrot | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) |
| Age | 10 | 4 | 13 | 15 | 2 | 1 | 8 | 6 |
A parrot breeder does not know the ages of these 8 parrots. She examines each of these 8 parrots and is asked to put them in order of decreasing age. She puts them in the order
$$\begin{array} { l l l l l l l l }
D & G & H & C & A & B & F & E
\end{array}$$
- Find, to 3 decimal places, Spearman's rank correlation coefficient between the breeder's order and the actual order.
(5) - Use your value of Spearman's rank correlation coefficient to test for evidence of the breeder's ability to order parrots correctly, by their age, after examining them. Use a \(1 \%\) significance level and state your hypotheses clearly.