Standard +0.3 This is a straightforward application of the product moment correlation coefficient hypothesis test with all summary statistics provided. Students need to calculate r using the standard formula, then perform a one-tailed test at 1% significance level. While it involves careful arithmetic with the given summations, it requires no conceptual insight beyond applying a standard procedure taught in FM Statistics, making it slightly easier than average.
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. [0pt]
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.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Statistics 2022 Q2 [7]}}