AQA S2 2012 January — Question 3

Exam BoardAQA
ModuleS2 (Statistics 2)
Year2012
SessionJanuary
TopicChi-squared distribution
3
  1. Table 1 contains the observed frequencies, \(a , b , c\) and \(d\), relating to the two attributes, \(X\) and \(Y\), required to perform a \(\chi ^ { 2 }\) test. \begin{table}[h]
    \captionsetup{labelformat=empty} \caption{Table 1}
    \cline { 2 - 4 } \multicolumn{1}{c|}{}\(\boldsymbol { Y }\)Not \(\boldsymbol { Y }\)Total
    \(\boldsymbol { X }\)\(a\)\(b\)\(m\)
    Not \(\boldsymbol { X }\)\(c\)\(d\)\(n\)
    Total\(p\)\(q\)\(N\)
    \end{table}
    1. Write down, in terms of \(m , n , p , q\) and \(N\), expressions for the 4 expected frequencies corresponding to \(a , b , c\) and \(d\).
    2. Hence prove that the sum of the expected frequencies is \(N\).
  2. Andy, a tennis player, wishes to investigate the possible effect of wind conditions on the results of his matches. The results of his matches for the 2011 season are represented in Table 2. \begin{table}[h]
    \captionsetup{labelformat=empty} \caption{Table 2}
    \cline { 2 - 4 } \multicolumn{1}{c|}{}WindyNot windyTotal
    Won151833
    Lost12517
    Total272350
    \end{table} Conduct a \(\chi ^ { 2 }\) test, at the \(10 \%\) level of significance, to investigate whether there is an association between Andy's results and wind conditions.
    (8 marks)
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