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2 marksSampling Distribution and Estimation

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

A sample of 45 farmers who adopted recommendations saved an average of 950 per month, with a sample standard deviation of 135.

Determine an unbiased estimate of the standard deviation.

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  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)(ii)Construct, without using a continuity correction, a 95% confidence interval for the mean amount of money saved.[4 marks]
  3. 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]
  4. 5(b)(iii)b)State which method is better and give a reason for your answer.[2 marks]
  5. 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]
  6. 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…[2 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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