Inference using normal and t-distributions – Further Probability & Statistics Paper 4

Candidates should be able to:

  • formulate hypotheses and apply a hypothesis test concerning the population mean using a small sample drawn from a normal population of unknown variance, using a t-test;
  • calculate a pooled estimate of a population variance from two samples (calculations based on either raw or summarised data may be required);
  • formulate hypotheses concerning the difference of population means, and apply, as appropriate:
    • a 2-sample t-test,
    • a paired sample t-test,
    • a test using a normal distribution
    • (the ability to select the test appropriate to the circumstances of a problem is expected);
  • determine a confidence interval for a population mean, based on a small sample from a normal population with unknown variance, using a t-distribution;
  • determine a confidence interval for a difference of population means, using a t-distribution, or a normal distribution, as appropriate.

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