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2 marksSampling Distribution and Estimation

CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2 · Question 5(c)

A 90% confidence interval for population mean, μ, is found for each sample when 60 random samples of size 45 are taken. Determine the expected number of intervals that do NOT contain μ.

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Other parts of this question

  1. 5(a)Explain what is meant by the term "a 95% confidence interval" in the context of a population mean.[2 marks]
  2. 5(b)(i)Determine an unbiased estimate of the standard deviation.[2 marks]
  3. 5(b)(ii)Construct, without using a continuity correction, a 95% confidence interval for the mean amount of money saved.[4 marks]
  4. 5(b)(iii)a)If the consultant considers that a 95% confidence interval is too wide, state TWO methods that can be taken to reduce this width.[2 marks]
  5. 5(b)(iii)b)State which method is better and give a reason for your answer.[2 marks]
  6. 5(b)(iv)Determine the least number of farmers that must be sampled so that the width of a 99% confidence interval is less than 40.[4 marks]
  7. 5(d)(i)State the distribution modelled by X̄ giving its parameters.[2 marks]
  8. 5(d)(ii)Calculate P(X̄ > 4.5).[5 marks]

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