Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions.
Understanding
- I can explain when a question needs a two-sample z-test for p₁ − p₂ rather than a one-sample test or an interval. (Guide: “When the question compares two proportions”; Practice Q1)
- I can explain why the test uses the pooled proportion p̂c, while the interval does not. (Guide: “The pooled proportion”; Practice Q7)
- I can explain what “independent samples” means and recognise paired or before-and-after data that are not independent. (Guide: Worked example 3; Practice Q7)
Skills
- I can name the procedure in full: two-sample z-test for the difference between two population proportions. (Guide: Worked examples 1 and 2; Practice Q5)
- I can define p₁ and p₂ with the response and each population, or each treatment in an experiment. (Guide: “Defining the parameters”; Practice Q4, Q5)
- I can write H₀ and a one-sided or two-sided Hₐ in both the p₁ = p₂ and the p₁ − p₂ = 0 forms. (Guide: “Writing the hypotheses”; Practice Q2)
- I can calculate p̂c = (x₁ + x₂)/(n₁ + n₂) and check all four counts against 10. (Guide: Worked example 1; Practice Q3, Q4)
- I can check the randomization and 10% conditions with numbers, and say when the 10% condition is not needed. (Guide: “The three conditions”; Practice Q5)
Reasoning
- I can choose the direction of Hₐ from the wording of the question, not from the data. (Guide: Worked example 1; Practice Q2, Q6)
- I can decide when a condition fails and explain why the z-test is then not appropriate. (Guide: Worked example 3; Practice Q3, Q7)
- I can find and correct errors in someone else’s test set-up. (Practice Q6)
All ticked? Move on to Topic 3.13, Carrying Out a Test for the Difference Between Two Population Proportions, or return to the course roadmap.