OCR MEI S2 2009 June — Question 1 16 marks

Exam BoardOCR MEI
ModuleS2 (Statistics 2)
Year2009
SessionJune
Marks16
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicHypothesis test of Pearson’s product-moment correlation coefficient
TypeCalculate PMCC from summary statistics
DifficultyStandard +0.3 This is a straightforward application of the PMCC formula with given summary statistics, followed by a standard hypothesis test using critical values from tables. The conceptual parts (iii-iv) require understanding of test assumptions and tail choice, but these are standard textbook points. Slightly above average due to the multi-part nature and need to interpret statistical concepts, but all techniques are routine for S2.
Spec5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation
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. $$\Sigma x = 2331.3 \quad \Sigma y = 6724.3 \quad \Sigma x ^ { 2 } = 111984 \quad \Sigma y ^ { 2 } = 921361 \quad \Sigma x y = 316345 \quad n = 50$$ \includegraphics[max width=\textwidth, alt={}, center]{ae79cdd9-a57c-490e-a9f3-f47c7c8a1aa6-2_857_905_516_621}
  1. Calculate the sample product moment correlation coefficient.
  2. 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.
  3. 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.
  4. 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.
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.

$$\Sigma x = 2331.3 \quad \Sigma y = 6724.3 \quad \Sigma x ^ { 2 } = 111984 \quad \Sigma y ^ { 2 } = 921361 \quad \Sigma x y = 316345 \quad n = 50$$

\includegraphics[max width=\textwidth, alt={}, center]{ae79cdd9-a57c-490e-a9f3-f47c7c8a1aa6-2_857_905_516_621}\\
(i) Calculate the sample product moment correlation coefficient.\\
(ii) 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.\\
(iii) 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.\\
(iv) 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.

\hfill \mbox{\textit{OCR MEI S2 2009 Q1 [16]}}
This paper (4 questions)
View full paper
Q1 16 Q2 19 Q3 20 Q4 17