A master sommelier is judging the maturation periods of 8 unique vintage wines from a vineyard. The actual maturation periods, in months, for the 8 wines are given in the following table:
WineABCDEFGHMaturation (months)5412386224451830\begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text{Wine} & A & B & C & D & E & F & G & H \\ \hline \text{Maturation (months)} & 54 & 12 & 38 & 62 & 24 & 45 & 18 & 30 \\ \hline \end{array}WineMaturation (months)A54B12C38D62E24F45G18H30
The sommelier is asked to list the wines in descending order of their maturation period (from the oldest to the youngest). She provides the following sequence:
D,F,C,A,E,H,G,B D, F, C, A, E, H, G, B D,F,C,A,E,H,G,BCalculate Spearman’s rank correlation coefficient between the sommelier's perceived order and the actual order, giving your answer to 3 decimal places.
Test, at the 5% significance level, whether there is evidence of a positive correlation between the sommelier's estimates and the true maturation periods. State your hypotheses clearly.
