One-Sample Hypothesis Test for Proportions: Fresh Take

  • Complete a one-sample [latex]z[/latex]-test for proportions from hypotheses to conclusions
  • Use a P-value to explain the conclusions of a completed [latex]z[/latex]-test for proportions
Steps for Hypothesis Testing

  1. Write out the null and alternative hypotheses.
  2. Check the conditions for the hypothesis test.
  3. Calculate a test statistic.
  4. Calculate a P-value.
  5. Compare the P-value to the significance level, [latex]\alpha[/latex], to make a decision.
  6. Write a conclusion in context (e.g., we do/do not have convincing evidence…).

You have learned that all hypothesis tests result in one of two actions: either you reject the null hypothesis in favor of the alternative OR you do not reject the null hypothesis.

Thus, at the end of this drug study, you will choose one of the following:

  • Reject the null hypothesis – There is evidence that the proportion of people taking the drug who have a second heart attack is less than [latex]0.15[/latex]. There is evidence the drug works!
  • Do NOT reject the null hypothesis – There is not sufficient evidence to declare that the proportion of people taking the drug who have a second heart attack is less than [latex]0.15[/latex]. There is not sufficient evidence to say the drug works.
Consider a court system analogy[1]: a person on trial is assumed to be innocent, the default/null belief ([latex]H_0[/latex]), until proven guilty through evidence ([latex]H_A[/latex]).There are two possible outcomes at the end of the trial:

  • There is enough evidence to reject the person’s innocence (Reject [latex]H_0[/latex]).
  • There is not enough evidence to reject the person’s innocence (Fail to Reject [latex]H_0[/latex]).

It is important to note that you cannot “accept [latex]H_0[/latex].” It’s assumed to be true already, so our research isn’t proving the null hypothesis. This is why a person is declared “not guilty” rather than “innocent” in court—their innocence was assumed at the beginning.

  1. Skew the Script. (2021). AP® Statistics Lessons. https://skewthescript.org/ap-stats-curriculum ↵