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3 marksSampling Distribution and Estimation

CAPE Applied Mathematics Unit 1 · 2013 · Paper 2 · Question 5(a)(i)

Random variable X is normally distributed with mean 35 and standard deviation 10. A sample of 8 observations is taken.

State the distribution of the sample mean, X̄, giving the value of its parameters.

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  1. 5(a)(ii)Calculate P(X̄ ≥ 38.7).[5 marks]
  2. 5(b)(i)Calculate a 94 per cent confidence interval for the true mean mass, µ, of the packages.[4 marks]
  3. 5(b)(ii)40 random samples of the packages of biscuits were taken, and a 94 per cent confidence interval for µ was found for each. Determine the expected number of…[2 marks]
  4. 5(c)(i)State TWO conditions why a t-test will be appropriate to test the hypothesis that the machine is not dispensing on average 10 ounces of coffee.[2 marks]
  5. 5(c)(ii)Formulate suitable null and alternative hypotheses (using statistical symbols) to test whether the mean amount of coffee dispensed is 10 ounces or whether it…[2 marks]
  6. 5(c)(iii)Test at the 5% level of significance whether the machine is dispensing on average 10 ounces of coffee.[7 marks]

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