5 Sixteen candidates took an examination paper in mechanics and an examination paper in statistics.
- For all sixteen candidates, the value of the product moment correlation coefficient \(r\) for the marks on the two papers was 0.701 correct to 3 significant figures.
Test whether there is evidence, at the \(5 \%\) significance level, of association between the marks on the two papers.
- A teacher decided to omit the marks of the candidates who were in the top three places in mechanics and the candidates who were in the bottom three places in mechanics. The marks for the remaining 10 candidates can be summarised by
\(n = 10 , \sum x = 750 , \sum y = 690 , \sum x ^ { 2 } = 57690 , \sum y ^ { 2 } = 49676 , \sum x y = 50829\).
- Calculate the value of \(r\) for these 10 candidates.
- What do the two values of \(r\), in parts (a) and (b)(i), tell you about the scores of the sixteen candidates?