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2 marksSampling Distribution and Estimation

CAPE Applied Mathematics Unit 1 · 2016 · Paper 2 · Question 5(a)(iv)

Time x to pepper seed germination is normally distributed with mean µ and standard deviation σ. A sample of n = 49 yields ∑x = 510 and ∑x^2 = 5635.

Sixty random samples of 49 pepper seeds are taken and a 95% confidence interval for µ is found for each sample. Determine the appropriate number of intervals that will contain the population mean, µ.

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  1. 5(a)(i)Calculate unbiased estimates for the population mean, µ.[2 marks]
  2. 5(a)(ii)Calculate unbiased estimates for the standard deviation, σ, of the length of time between planting and germination.[3 marks]
  3. 5(a)(iii)Construct a 94% confidence interval for the mean length of time it takes for this type of pepper seed to germinate.[3 marks]
  4. 5(b)The mean of 150 observations of X, where X ~ Bin(135, 0.36) is X̄. Use the central limit theorem to state the distribution that is modelled by X̄, giving the…[5 marks]
  5. 5(c)(i)State, in symbols, appropriate null and alternative hypotheses for the test.[3 marks]
  6. 5(c)(ii)Determine the critical region(s) for the test.[3 marks]
  7. 5(c)(iii)Calculate the value of the test statistic.[2 marks]
  8. 5(c)(iv)State your conclusions, giving reasons.[2 marks]

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