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4 marksSampling Distribution and Estimation

CAPE Applied Mathematics Unit 1 · 2021 · Paper 2 · Question 6(b)

Confidence interval for a population proportion.

A random sample of 384 provided a 95% confidence interval for a population proportion, p, with a margin of error of 0.05. Approximate the value of p based on this information.

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Other parts of this question

  1. 6(a)(i)Formulate the null and alternative hypotheses for the chi-square test.[2 marks]
  2. 6(a)(ii)Complete the table to show the missing expected frequencies and marginal totals.[4 marks]
  3. 6(a)(iii)Calculate the chi-square test statistic value.[3 marks]
  4. 6(a)(iv)Determine the critical region of the test at the 5% level of significance.[3 marks]
  5. 6(a)(v)State clearly the conclusion that may be drawn from this test.[2 marks]
  6. 6(c)(i)Calculate the sample mean and sample variance for these observations.[3 marks]
  7. 6(c)(ii)Determine the critical region for a test of H0: mu = 14.0 against H1: mu != 14.0 at the 5% significance level.[4 marks]

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