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3 marksSampling Distribution and Estimation

CAPE Applied Mathematics Unit 1 · 2011 · Paper 2 · Question 6(a)

X is a non-normal population with mean 100 and variance 16. Fifty observations of X are taken.

State the approximate distribution of X̄ giving its parameters.

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  1. 6(b)Given that the critical value for χ² is 9.488, use your tables to determine the degrees of freedom and the significance level.[3 marks]
  2. 6(c)(i)Formulate null and alternate hypotheses for this test.[2 marks]
  3. 6(c)(ii)Calculate the expected frequencies, E, when the null hypothesis is true.[5 marks]
  4. 6(c)(iii)a)Determine the number of degrees of freedom.[2 marks]
  5. 6(c)(iii)b)Determine the critical region.[2 marks]
  6. 6(c)(iii)c)Calculate the test statistic.[5 marks]
  7. 6(c)(iv)State clearly, with reason, your conclusion of the test.[3 marks]

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