1 The best performances of a random sample of 20 junior athletes in the long jump, \(x\) metres, and in the high jump, \(y\) metres, were recorded. The following statistics were calculated from the results.
$$S _ { x x } = 7.0036 \quad S _ { y y } = 0.8464 \quad S _ { x y } = 1.3781$$
- Calculate the value of the product moment correlation coefficient between \(x\) and \(y\).
(2 marks) - Assuming that these data come from a bivariate normal distribution, investigate, at the \(1 \%\) level of significance, the claim that for junior athletes there is a positive correlation between \(x\) and \(y\).
- Interpret your conclusion in the context of this question.