Edexcel S4 2002 June — Question 7

Exam BoardEdexcel
ModuleS4 (Statistics 4)
Year2002
SessionJune
TopicHypothesis test of binomial distributions
TypeFind or state significance level
  1. A proportion \(p\) of the items produced by a factory is defective. A quality assurance manager selects a random sample of 5 items from each batch produced to check whether or not there is evidence that \(p\) is greater than 0.10 . The criterion that the manager uses for rejecting the hypothesis that \(p\) is 0.10 is that there are more than 2 defective items in the sample.
    1. Find the size of the test.
      (2)
    Table 1 gives some values, to 2 decimal places, of the power function of this test. \begin{table}[h]
    \captionsetup{labelformat=empty} \caption{Table 1}
    \(p\)0.150.200.250.300.350.40
    Power0.03\(r\)0.100.160.240.32
    \end{table}
  2. Find the value of \(r\). One day the manager is away and an assistant checks the production by random sample of 10 items from each batch produced. The hypothesis that \(p = 0.10\) is rejected if more than 4 defectives are found in the sample.
  3. Find P (Type I error) using the assistant's test. Table 2 gives some values, to 2 decimal places, of the power function for this test. \begin{table}[h]
    \captionsetup{labelformat=empty} \caption{Table 2}
    \(p\)0.150.200.250.300.350.40
    Power0.010.030.080.150.25\(s\)
    \end{table}
  4. Find the value of \(s\).
  5. Using the same axes, draw the graphs of the power functions of these two tests.
    1. State the value of \(p\) where these graphs cross.
    2. Explain the significance if \(p\) is greater than this value. The manager studies the graphs in part ( \(e\) ) but decides to carry on using the test based on a sample of size 5 .
  7. Suggest 2 reasons why the manager might have made this decision.
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