What is a hypothesis test using a Poisson distribution?

• You can use?a Poisson distribution?to test whether the?mean number of occurrences?for a?given time period?within a population has?increased?or?decreased
  • These tests will always be?one-tailed
  • You will not be expected to perform a two-tailed hypothesis test with the Poisson distribution

What are the steps for a hypothesis test of a Poisson proportion?

• STEP 1:?Write the hypotheses
  • H_0?:?m?=?m₀
    • Clearly state that?m?represents the?mean number of occurrences?for the?given time period
    • m₀?is the?assumed mean number of occurrences
    • You might have to use?proportion?to find?m₀
  • H_1?:?m?<?m_0?or H_1?:?m?>?m₀

• STEP 2: Calculate the?p-value?or find the?critical region
  • See below
• STEP 3:?Decide?whether there is?evidence to reject the null hypothesis
  • If the?p-value < significance level then reject H₀
  • If the test statistic is in the critical region then reject H₀
• STEP 4:?Write your conclusion
  • If you?reject H₀-?then there is evidence to suggest that...
    • The mean number of occurrences has decreased (for H_1?:?m?<?m₀)
    • The mean number of occurrences has increased (for H_1?:?m?>?m₀)
  • If you?accept H-_0?then there is?insufficient evidence?to reject the null hypothesis which suggests that...
    • The mean number of occurrences has not decreased (for H_1?:?m?<?m₀)
    • The mean number of occurrences has not increased (for H_1?:m?>?m₀)

How do I calculate the?p-value?

• The?p-value is determined by the?test statistic?x
• The?p-value is the probability that ‘a value being?at least as extreme?as the test statistic’ would occur if?null hypothesis were true

How do I find the critical value and critical region?

• The critical value and critical region are determined by the?significance level?α%
• Your calculator might have an?inverse Poisson function?that works just like the inverse normal function
  • You need to use this value to find the critical value
  • The value given by the inverse Poisson function is normally one away from the actual critical value