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6 marksSampling Distribution and Estimation

CAPE Applied Mathematics Unit 1 · 2008 · Paper 2 · Question 5(a)

The probability that a primary school pupil plays cricket is p. In a random sample of 400 pupils, 192 play cricket.

Omitting the continuity correction, calculate an approximate 97% confidence interval for p.

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Other parts of this question

  1. 5(b)(i)Using symbols only, state appropriate null and alternative hypotheses.[4 marks]
  2. 5(b)(ii)Justify the use of a normal distribution approximation in this large-sample test of a binomial proportion.[2 marks]
  3. 5(b)(iii)State the critical region(s) for this test.[4 marks]
  4. 5(b)(iv)Using an appropriate continuity correction, calculate the test statistic.[6 marks]
  5. 5(b)(v)Supporting your answer with a reasoned argument, state the conclusion that may be drawn from the hypothesis test.[3 marks]

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