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3 marksHypothesis Testing

CAPE Applied Mathematics Unit 1 · 2017 · Paper 2 · Question 6(a)(i)

The mass of bags of sugar packed by a machine follows a normal distribution with mean 250 g and standard deviation 5 g. A sample of 50 bags taken after servicing gives a mean mass of 251.9 g. Test at the 5% level of significance whether the mean mass has changed.

State clearly the null and alternate hypotheses.

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Other parts of this question

  1. 6(a)(ii)Identify the critical region(s) of the test statistic.[4 marks]
  2. 6(a)(iii)Calculate the value of the test statistic.[4 marks]
  3. 6(a)(iv)State clearly a valid conclusion of the test, giving a reason for your answer.[3 marks]
  4. 6(b)(i)State clearly the null and alternative hypotheses.[2 marks]
  5. 6(b)(ii)Calculate, to the nearest whole number, the expected number of males that have no opinion.[3 marks]
  6. 6(b)(iii)Identify the rejection region of the test.[3 marks]
  7. 6(b)(iv)The calculated chi-square value of the test is 9.8249. State clearly the conclusion for this test, giving a reason for your answer.[3 marks]

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