Hypothesis tests

You will be able to

• Formulate H₀ and H₁ (one- or two-tailed) and find the critical and acceptance regions for a single observation from a binomial or Poisson distribution by direct evaluation.
• Find a critical region using the normal approximation with a continuity correction, or for the mean of a normal population with known variance.
• State the actual probability of rejecting a true H₀ and write the conclusion of the test in context.

You will be able to

• State what Type I and Type II errors mean in the context of a test, and calculate P(Type I error) as the actual significance level.
• Calculate the probability of a Type II error for a given true value, for a binomial or Poisson test by direct evaluation and for a test of a mean with known variance.
• Explain how the two error probabilities change when the significance level, the sample size or the true value changes.