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3 marksHypothesis Testing

CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2 · Question 5(b)(iii)

In 180 tosses of a pair of dice, a sum of 9 occurred 12 times. A hypothesis test at the 5% significance level checks if the dice are biased to produce fewer 9s.

Determine the critical region for this hypothesis test at the 5% significance level.

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Other parts of this question

  1. 5(a)(i)a)Calculate the unbiased estimate of the population mean.[2 marks]
  2. 5(a)(i)b)Calculate the unbiased estimate of the population standard deviation.[3 marks]
  3. 5(a)(ii)a)For testing H0: mu = 45 versus H1: mu < 45 at the 5% significance level, determine the critical region.[3 marks]
  4. 5(a)(ii)b)Calculate the value of the test statistic for this hypothesis test.[3 marks]
  5. 5(a)(ii)c)Clearly state the conclusion of the test.[1 mark]
  6. 5(b)(i)Calculate the theoretical probability of rolling a sum of 9 with a pair of fair dice.[2 marks]
  7. 5(b)(ii)State in symbols the null and alternative hypotheses for testing if the dice yield fewer 9s than expected.[2 marks]
  8. 5(b)(iv)Calculate the appropriate test statistic.[5 marks]
  9. 5(b)(v)Clearly state the conclusion drawn from the test.[1 mark]

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