AQA S1 2011 June — Question 7

Exam BoardAQA
ModuleS1 (Statistics 1)
Year2011
SessionJune
TopicBivariate data
TypeInterpret correlation coefficient value
7
  1. Three airport management trainees, Ryan, Sunil and Tim, were each instructed to select a random sample of 12 suitcases from those waiting to be loaded onto aircraft. Each trainee also had to measure the volume, \(x\), and the weight, \(y\), of each of the 12 suitcases in his sample, and then calculate the value of the product moment correlation coefficient, \(r\), between \(x\) and \(y\).
    • Ryan obtained a value of - 0.843 .
    • Sunil obtained a value of + 0.007 .
    Explain why neither of these two values is likely to be correct.
  2. Peggy, a supervisor with many years' experience, measured the volume, \(x\) cubic feet, and the weight, \(y\) pounds, of each suitcase in a random sample of 6 suitcases, and then obtained a value of 0.612 for \(r\).
    • Ryan and Sunil each claimed that Peggy's value was different from their values because she had measured the volumes in cubic feet and the weights in pounds, whereas they had measured the volumes in cubic metres and the weights in kilograms.
    • Tim claimed that Peggy's value was almost exactly half his calculated value because she had used a sample of size 6 whereas he had used one of size 12 .
    Explain why neither of these two claims is valid.
  3. Quentin, a manager, recorded the volumes, \(v\), and the weights, \(w\), of a random sample of 8 suitcases as follows.
    \(\boldsymbol { v }\)28.119.746.423.631.117.535.813.8
    \(\boldsymbol { w }\)14.912.121.118.019.819.216.214.7
    1. Calculate the value of \(r\) between \(v\) and \(w\).
    2. Interpret your value in the context of this question.
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