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5 marksSampling Distribution and Estimation

CAPE Applied Mathematics Unit 1 · 2021 · Paper 2 · Question 5(a)(i)

Weights of bags of apples follow a normal distribution with mean mu and variance sigma^2. A sample of 150 bags gives sum(x) = 1600 and sum(x^2) = 18040.

Calculate unbiased estimates for the mean and standard deviation of X.

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Other parts of this question

  1. 5(a)(ii)State an appropriate distribution for the sample mean, X-bar.[2 marks]
  2. 5(a)(iii)Determine an approximate 95% confidence interval for the unknown population mean, mu.[3 marks]
  3. 5(a)(iv)Formulate the null and alternative hypotheses.[2 marks]
  4. 5(a)(v)Determine the critical value for the test.[1 mark]
  5. 5(a)(vi)Determine the rejection region.[1 mark]
  6. 5(a)(vii)Given that the test statistic is -1.59, state clearly a valid conclusion for the test.[2 marks]
  7. 5(b)(i)Identify the distribution that can be used to model this situation, giving ONE reason.[2 marks]
  8. 5(b)(ii)Determine the critical value.[2 marks]
  9. 5(b)(iii)Determine the rejection region.[1 mark]
  10. 5(b)(iv)Given that the mean is 30.5 and the standard deviation is 10.6, calculate the test statistic.[2 marks]
  11. 5(b)(v)State clearly a valid conclusion for the test.[2 marks]

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