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3 marksSampling Distribution and Estimation

CAPE Applied Mathematics Unit 1 · 2014 · Paper 2 · Question 5(a)(i)a)

The minutes late for a sample of 12 students are: 3, 13, 5, 8, 12, 5, 6, 4, 8, 7, 10, 8.

Calculate an unbiased estimator for the mean number of minutes students arrive late.

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  1. 5(a)(i)b)Calculate an unbiased estimator for the variance of the minutes students arrive late.[4 marks]
  2. 5(a)(ii)a)State in statistical symbols the null and alternative hypotheses.[2 marks]
  3. 5(a)(ii)b)Determine the critical region for the test.[4 marks]
  4. 5(a)(ii)c)Calculate the value of the test statistic.[3 marks]
  5. 5(a)(ii)d)Clearly state the conclusion of this hypothesis test.[2 marks]
  6. 5(a)(ii)e)State the assumption required to perform this test.[1 mark]
  7. 5(b)In a sample of 52 students, 18 arrived late for class. Construct a 95% confidence interval for the population proportion of students who arrive late.[6 marks]

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