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Question involves comparing or contrasting Spearman's rank correlation coefficient with Pearson's product moment correlation coefficient, or discussing when each is appropriate.

3 questions · Moderate -0.1

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OCR MEI Paper 2 2024 June Q11
5 marks Moderate -0.8
11 A householder is investigating whether there is any relationship between his monthly cost of gas and his monthly cost of electricity, both measured in pounds ( \(\pounds\) ). The householder collects a random sample of monthly costs and presents them in the scatter diagram below. \includegraphics[max width=\textwidth, alt={}, center]{8e48bbd3-2166-49e7-8906-833261f331ca-08_604_1452_392_244} One of the points on the diagram represents the energy costs in a month when the householder was away on holiday for three weeks. The other points represent the energy costs in months when the householder did not go away on holiday.
  1. On the copy of the diagram in the Printed Answer Booklet, circle the point which represents the month when the householder was most likely to have been away on holiday for three weeks.
  2. With reference to the diagram, describe the relationship between the cost of gas and the cost of electricity. The householder decides to test whether there is evidence to suggest that there is any association between the monthly cost of gas and the monthly cost of electricity. The value of Spearman's rank correlation coefficient for this sample is 0.4359 and the associated \(p\)-value is 0.09195 .
  3. Determine whether there is any evidence to suggest, at the \(5 \%\) level, that there is any association between the monthly cost of gas and the monthly cost of electricity.
OCR MEI Further Statistics Major Specimen Q6
3 marks Standard +0.3
6 Fig. 6 shows the wages earned in the last 12 months by each of a random sample of American males aged between 16 and 65 . \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e6ee3a4a-3e76-4422-9a78-17b64b458f83-07_771_1278_340_392} \captionsetup{labelformat=empty} \caption{Fig. 6}
\end{figure} A researcher wishes to test whether the sample provides evidence of a tendency for higher wages to be earned by older men in the age range 16 to 65 in America.
  1. The researcher needs to decide whether to use a test based on Pearson's product moment correlation coefficient or Spearman's rank correlation coefficient. Use the information in Fig. 6 to decide which test is more appropriate.
  2. Should it be a one-tail or a two-tail test? Justify your answer.
OCR S1 2013 January Q7
7 marks Standard +0.3
  1. Two judges rank \(n\) competitors, where \(n\) is an even number. Judge 2 reverses each consecutive pair of ranks given by Judge 1, as shown.
    Competitor\(C_1\)\(C_2\)\(C_3\)\(C_4\)\(C_5\)\(C_6\)\(\ldots\)\(C_{n-1}\)\(C_n\)
    Judge 1 rank123456\(\ldots\)\(n-1\)\(n\)
    Judge 2 rank214365\(\ldots\)\(n\)\(n-1\)
    Given that the value of Spearman's coefficient of rank correlation is \(\frac{63}{65}\), find \(n\). [4]
  2. An experiment produced some data from a bivariate distribution. The product moment correlation coefficient is denoted by \(r\), and Spearman's rank correlation coefficient is denoted by \(r_s\).
    1. Explain whether the statement $$r = 1 \Rightarrow r_s = 1$$ is true or false. [1]
    2. Use a diagram to explain whether the statement $$r \neq 1 \Rightarrow r_s \neq 1$$ is true or false. [2]