1 An investment analyst thinks that there may be correlation between the cost of oil, \(x\) dollars per barrel, and the price of a particular share, \(y\) pence. The analyst selects 50 days at random and records the values of \(x\) and \(y\). Summary statistics for these data are shown below, together with a scatter diagram.
$$\Sigma x = 2331.3 \quad \Sigma y = 6724.3 \quad \Sigma x ^ { 2 } = 111984 \quad \Sigma y ^ { 2 } = 921361 \quad \Sigma x y = 316345 \quad n = 50$$
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- Calculate the sample product moment correlation coefficient.
- Carry out a hypothesis test at the \(5 \%\) significance level to investigate the analyst's belief. State your hypotheses clearly, defining any symbols which you use.
- An assumption that there is a bivariate Normal distribution is required for this test to be valid. State whether it is the sample or the population which is required to have such a distribution. State, with a reason, whether in this case the assumption appears to be justified.
- Explain why a 2-tail test is appropriate even though it is clear from the scatter diagram that the sample has a positive correlation coefficient.