A-Level Maths Edexcel 9MA0

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#3 Use binomial distribution in hypothesis testing

You can use the binomial distribution to perform a hypothesis test if the conditions for a binomially distributed event are met:

  • there is a fixed number of trials (n),
  • there are only two possible outcomes (success and failure),
  • there is a fixed probability of success (p), and
  • the trials are independent of each other.

To perform the test:

  • Define the test statistic
  • Determine whether a one-tailed or two-tailed test is needed
  • Identify the null and alternate hypotheses accordingly
  • Calculate the probability of the test statistic taking the observed value or higher/lower, assuming the null hypothesis to be true
  • Compare this to the significance level, and either reject or cannot reject the null hypothesis
  • Conclude with a statement in context of the question