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8 markst-test

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

Battery life claimed to be 3.5 hours. A sample of 8 laptops gave battery lives (in hours): 3.4, 3.7, 3.1, 3.2, 3.6, 3.5, 3.3, 3.4 (sum x = 27.2, sum x^2 = 92.76).

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 alternative hypotheses, b) test value, c) critical region, d) conclusion.

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Other parts of this question

  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(b)Calculate a 98% confidence interval for the mean length of the pencils produced by the machine.[4 marks]
  4. 5(c)(i)Calculate an unbiased estimate for the standard deviation of the lifetime of the battery of the computer.[4 marks]
  5. 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]

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