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2 marksHypothesis Testing

CAPE Applied Mathematics Unit 1 · 2015 · Paper 2 · Question 5(c)(i)

Spice package masses are normally distributed with mean 48 g and standard deviation 2.3 g. A sample of 49 packages after machine repairs has mean 47.2 g with unchanged standard deviation.

State null and alternative hypotheses, using statistical symbols to test whether the mean mass has changed.

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Other parts of this question

  1. 5(a)(i)Calculate the width of the interval.[2 marks]
  2. 5(a)(ii)Calculate the mean of the sample.[2 marks]
  3. 5(a)(iii)Calculate the standard deviation of the value of the sales invoice.[3 marks]
  4. 5(b)(i)State the approximate distribution modelled by X̄, giving its parameters.[3 marks]
  5. 5(b)(ii)Calculate P(X̄ < 28).[5 marks]
  6. 5(c)(ii)Determine the critical region(s) of the test conducted at the 4% significance level.[3 marks]
  7. 5(c)(iii)Calculate the value of the test statistic used in this test.[3 marks]
  8. 5(c)(iv)Clearly state the conclusion of the test.[2 marks]

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