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CAPE Applied Mathematics Unit 1 · 2010 · Paper 2 · Question 6(b)(iii)

A machine is set to produce packages of sweets with a mean mass of 150 g. A random sample of 15 packages has a mean mass of 158 g and a standard deviation of 43 g. A t-test is carried out at the 5% level of significance to test if the mean mass has increased.

Identify the critical region for this test.

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Other parts of this question

  1. 6(a)(i)State clearly the null and alternative hypotheses.[2 marks]
  2. 6(a)(ii)a)Calculate, to the nearest whole number, the expected number of textbooks with hard back covers.[2 marks]
  3. 6(a)(ii)b)Calculate, to the nearest whole number, the expected number of novels with paper back covers.[2 marks]
  4. 6(a)(iii)Identify the rejection region for this test.[2 marks]
  5. 6(a)(iv)The calculated χ² value is 9.2649. State clearly the conclusion of this test.[2 marks]
  6. 6(b)(i)State the assumption that must be made under which a t-test is valid.[1 mark]
  7. 6(b)(ii)State clearly the null and alternative hypotheses for the test.[3 marks]
  8. 6(b)(iv)Calculate the test statistic to be used in this test.[5 marks]
  9. 6(b)(v)State clearly the conclusion for this test, giving a reason for your answer.[3 marks]

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