Contingency table construction from description

A question is this type if and only if the contingency table is not fully given but must be constructed by the student from a written description of counts before the chi-squared test can be performed.

4 questions · Standard +0.3

5.06a Chi-squared: contingency tables
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OCR S3 2007 June Q4
9 marks Standard +0.3
4 The students in a large university department take a trial examination some time before the proper examination. A random sample of 60 students took both examinations during a particular course. 42 students passed the trial examination, 36 passed the proper examination and 13 failed both examinations.
  1. Copy and complete the following contingency table.
    Proper
    \cline { 2 - 4 } \multicolumn{1}{l}{}PassFailTotal
    \cline { 2 - 5 }Pass42
    \cline { 2 - 5 } TrialFail13
    \cline { 2 - 5 }Total3660
  2. Carry out a test of independence at the \(\frac { 1 } { 2 } \%\) level of significance.
AQA Further Paper 3 Statistics Specimen Q5
8 marks Standard +0.3
5 Students at a science department of a university are offered the opportunity to study an optional language module, either German or Mandarin, during their second year of study. From a sample of 50 students who opted to study a language module, 31 were female. Of those who opted to study Mandarin, 8 were female and 12 were male. Test, using the \(5 \%\) level of significance, whether choice of language is independent of gender. The sample of students may be regarded as random.
[0pt] [8 marks] Turn over for the next question
CAIE FP2 2010 June Q10
13 marks Standard +0.3
Three new flu vaccines, \(A\), \(B\) and \(C\), were tested on \(500\) volunteers. The vaccines were assigned randomly to the volunteers and \(178\) received \(A\), \(149\) received \(B\) and \(173\) received \(C\). During the following winter, of the volunteers given \(A\) caught flu, \(29\) of the volunteers given \(B\) caught flu, and \(16\) of the volunteers given \(C\) caught flu. Carry out a suitable test for independence at the \(5\%\) significance level. [10] Without using a statistical test, decide which of the vaccines appears to be most effective. [3]
Edexcel S3 Q6
15 marks Standard +0.3
A survey found that of the 320 people questioned who had passed their driving test aged under twenty-five, 104 had been involved in an accident in the two years following their test. Of the 80 people in the survey who were aged twenty-five or over when they passed their test, 16 had been involved in an accident in the following two years.
  1. Draw up a contingency table showing this information. [2]
It is desired to test whether the proportion of drivers having accidents within two years of passing their test is different for those who were aged under twenty-five at the time of passing their test than for those aged twenty-five or over.
    1. Stating your hypotheses clearly, carry out the test at the 5\% level of significance.
    2. Explain clearly why there is only one degree of freedom. [11]
It is found that 12 people who were aged under twenty-five when they took their test and had been involved in an accident in the following two years had been omitted from the information given.
  1. Explain why you do not need to repeat the calculation to know the correct result of the test. [2]