A wine sommelier is participating in a blind tasting study to evaluate their ability to estimate the maturation age of vintage wines. Eight distinct bottles of wine are presented to the sommelier. The actual ages, in years, of these 8 bottles are given in the table below:
Wine BottleABCDEFGHActual Age (years)154282550123020 \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text{Wine Bottle} & A & B & C & D & E & F & G & H \\ \hline \text{Actual Age (years)} & 15 & 42 & 8 & 25 & 50 & 12 & 30 & 20 \\ \hline \end{array} Wine BottleActual Age (years)A15B42C8D25E50F12G30H20The sommelier is asked to list the bottles in order of decreasing age (from oldest to youngest). They provide the following sequence:
E,G,B,H,D,F,A,C E, G, B, H, D, F, A, C E,G,B,H,D,F,A,CCalculate Spearman’s rank correlation coefficient between the sommelier's estimated order and the actual order of age, giving your answer to 3 decimal places.
Using your result from part (a), test at the 5% significance level whether there is evidence of a positive correlation between the sommelier's rankings and the true ages. State your hypotheses clearly.
