What is a hypothesis test using a binomial distribution?

• You can use?a binomial distribution?to test whether the?proportion?of a population with a specified characteristic 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 binomial distribution
    • This can be thought of as the number of successes

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

• STEP 1:?Write the hypotheses
  • H_0?:?p?=?p₀
    • Clearly state that?p?represents the?population proportion
    • p₀?is the?assumed population proportion
  • H_1?:?p?<?p_0?or H_1?:?p?>?p₀

• 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 population proportion has decreased (for H_1?:?p?<?p₀)
    • The population proportion has increased (for H_1?: ?p?>?p₀)
  • If you?accept H-_0?then there is?insufficient evidence?to reject the null hypothesis which suggests that...
    • The population proportion has not decreased (for H_1?:?p?<?p₀)
    • The population proportion has not increased (for H_1?:?p?>?p₀)

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 binomial 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 binomial function is normally one away from the actual critical value