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.
\(n = 12\)
\(\sum x ^ { 2 } = 28127\)
\(\sum x = 399\)
\(\Sigma y ^ { 2 } = 116509.0212\)
\(\Sigma y = 623.88\)
\(\sum x y = 45006.01\) Test at the \(1 \%\) significance level whether the shopper's estimates are positively correlated with the actual cost of the items.
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