Comment on test validity or assumptions

A question is this type if and only if it asks to discuss whether assumptions for the test are valid, or how certain conditions might affect the validity of the test.

3 questions · Standard +0.3

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Edexcel S3 2015 June Q3
11 marks Standard +0.3
  1. The number of accidents on a particular stretch of motorway was recorded each day for 200 consecutive days. The results are summarised in the following table.
Number of accidents012345
Frequency4757463596
  1. Show that the mean number of accidents per day for these data is 1.6 A motorway supervisor believes that the number of accidents per day on this stretch of motorway can be modelled by a Poisson distribution. She uses the mean found in part (a) to calculate the expected frequencies for this model. Her results are given in the following table.
    Number of accidents012345 or more
    Frequency40.3864.61\(r\)27.5711.03\(s\)
  2. Find the value of \(r\) and the value of \(s\), giving your answers to 2 decimal places.
  3. Stating your hypotheses clearly, use a \(10 \%\) level of significance to test the motorway supervisor's belief. Show your working clearly.
Edexcel S3 2017 June Q4
11 marks Standard +0.3
4. The number of emergency plumbing calls received per day by a local council was recorded over a period of 80 days. The results are summarised in the table below.
Number of calls, \(\boldsymbol { x }\)012345678
Frequency3131415108863
  1. Show that the mean number of emergency plumbing calls received per day is 3.5 A council officer suggests that a Poisson distribution can be used to model the number of emergency plumbing calls received per day. He uses the mean from the sample above and calculates the expected frequencies shown in the table below.
    \(\boldsymbol { x }\)01234567
    8 or
    more
    Expected
    frequency
    		2.428.4614.80\(r\)15.1010.576.173.08\(s\)
  2. Calculate the value of \(r\) and the value of \(s\), giving your answers correct to 2 decimal places.
  3. Test, at the \(5 \%\) level of significance, whether or not the Poisson distribution is a suitable model for the number of emergency plumbing calls received per day. State your hypotheses clearly.
Edexcel S3 2018 Specimen Q3
11 marks Standard +0.3
3. The number of accidents on a particular stretch of motorway was recorded each day for 200 consecutive days. The results are summarised in the following table.
Number of accidents012345
Frequency4757463596
  1. Show that the mean number of accidents per day for these data is 1.6 A motorway supervisor believes that the number of accidents per day on this stretch of motorway can be modelled by a Poisson distribution. She uses the mean found in part (a) to calculate the expected frequencies for this model. Her results are given in the following table.
    Number of accidents012345 or more
    Frequency40.3864.61\(r\)27.5711.03\(s\)
  2. Find the value of \(r\) and the value of \(s\), giving your answers to 2 decimal places.
  3. Stating your hypotheses clearly, use a \(10 \%\) level of significance to test the motorway supervisor's belief. Show your working clearly.