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4 marksSampling Distribution and Estimation

CAPE Applied Mathematics Unit 1 · 2012 · Paper 2 · Question 5(b)

The length of pencils is normally distributed with variance 0.25 mm^2. A sample of 45 pencils has mean length 75.9 mm.

Calculate a 98% confidence interval for the mean length of the pencils produced by the machine.

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  1. 5(a)(i)State the mean, the variance and the distribution of the mean, X̄, of the sample.[3 marks]
  2. 5(a)(ii)Calculate the probability that the sample mean is less than 417 grams.[4 marks]
  3. 5(c)(i)Calculate an unbiased estimate for the standard deviation of the lifetime of the battery of the computer.[4 marks]
  4. 5(c)(ii)State TWO conditions that are necessary for the valid use of a t-test to test a hypothesis about the mean of X.[2 marks]
  5. 5(c)(iii)Assuming a t-test is valid, test at the 5% significance level whether the advertisement was overstating the battery life. Clearly state: a) null and…[8 marks]

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