5 In a fashion competition, two judges gave marks to a large number of contestants. The value of Spearman's rank correlation coefficient, \(\mathrm { r } _ { \mathrm { s } }\), between the marks given to 7 randomly chosen contestants is \(\frac { 27 } { 28 }\).

1. An excerpt from the table of critical values of \(\mathrm { r } _ { \mathrm { s } }\) is shown below. \section*{Critical values of Spearman's rank correlation coefficient}

   	1-tail test	5\%	2.5\%	1\%	0.5\%
   	2-tail test	10\%	5\%	2\%	1\%
   \multirow{3}{*}{\(n\)}	6	0.8286	0.8857	0.9429	1.0000
   	7	0.7143	0.7857	0.8929	0.9286
   	8	0.6429	0.7381	0.8333	0.8810

   Test whether there is evidence, at the 1\% significance level, that the judges agree with each another. The marks given by the two judges to the 7 randomly chosen contestants were as follows, where \(x\) is an integer.

   Contestant	A	B	C	D	\(E\)	\(F\)	G
   Judge 1	64	65	67	78	79	80	86
   Judge 2	61	63	78	80	81	90	\(x\)

2. Use the value \(\mathrm { r } _ { \mathrm { s } } = \frac { 27 } { 28 }\) to determine the range of possible values of \(x\).
3. Give a reason why it might be preferable to use the product moment correlation coefficient rather than Spearman's rank correlation coefficient in this context.