2 A shopper estimates the cost, \(\pounds X\) per item, of each of 12 items in a supermarket. The shopper's estimates are compared with the actual cost, \(\pounds Y\) per item, of each item. The results are summarised as follows.
\(n = 12\)
\(\sum x = 399\)
\(\sum y = 623.88\)
\(\sum x ^ { 2 } = 28127\)
\(\sum y ^ { 2 } = 116509.0212\)
\(\sum x y = 45006.01\)
Test at the 1\% significance level whether the shopper's estimates are positively correlated with the actual cost of the items.