Hypothesis Testing

Scheme of work: Year 12 A-Level: Applied: Statistics: Hypothesis Testing

Prerequisite Knowledge

  • Use simple, discrete probability distributions, including the binomial distribution;
  • Identify the discrete uniform distribution;
  • Calculate probabilities using the binomial distribution.
  • Calculate cumulative probabilities using the binomial distribution

Success Criteria

  • Set up a null and alternative hypothesis based on a binomial distribution
  • Understand when to use a one- or two-tailed test.
  • Understand the importance of the significance level in a statistical test.
  • Test an observed value of a test statistic against the significance level.
  • Find a critical region or a test.

Teaching Points

  • When setting up the null and alternative hypotheses, students often find it helpful to draw a diagram detailing the significance level, critical region and whether it is a one- or two-tailed test.

One-Tailed Test 5% significance level

Two-Tailed Test 5% significance level

Two-Tailed Hypothesis Testing
  • Test conclusions must be written based on the context specified in the question.
  • When testing a hypothesis, students should test against the test statistic rather than finding the critical region, which often leads to errors in working.

Common Misconceptions

  • When summarizing a hypothesis test with the correct values, some students make an incorrect conclusion or do not conclude.
  • When identifying the critical region students often use incorrect notation.
  • Some students write their hypothesis in words rather than H0: p = 0.5 H1 : p >  0.5.
  • Students drop marks in exams through their notation; for instance, they write P(X < a) rather than P(X ≤ a)
  • Some students try to find the critical region when testing a hypothesis. Unfortunately, this method requires more detailed work, often leading to errors.

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