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 why one interval for p₁ − p₂ may or may not capture the true difference, and why I cannot tell which. (Guide: “What the interval is estimating”; Practice Q7)
- I can explain what a positive, a negative and a zero value of p₁ − p₂ mean in context. (Guide: “Interpreting the interval in context”; Practice Q3)
- I can explain why an interval that contains 0 is not evidence that the proportions are equal. (Guide: Worked example 2; Practice Q6)
Skills
- I can interpret a C% interval for p₁ − p₂ with the confidence level, both endpoints, the order of subtraction, the response and both populations or treatments. (Guide: Worked example 1; Practice Q5)
- I can interpret the confidence level as the long-run capture rate in repeated random sampling with the same sample sizes. (Guide: “Interpreting the confidence level”; Practice Q2, Q5)
- I can translate interval endpoints into percentage points. (Guide: “Interpreting the interval in context”; Practice Q3, Q6)
- I can recover the point estimate, margin of error and standard error from an interval and rebuild it at another confidence level. (Practice Q4)
- I can spot and correct wrong interpretations, such as “95% probability” or statements about individuals or samples. (Guide: Worked example 3; Practice Q2)
Reasoning
- I can use whether the interval contains 0 to decide whether there is convincing evidence of a difference. (Guide: “Using the interval to justify a claim”; Practice Q1)
- I can use the signs of the endpoints to justify a claim about which proportion is larger. (Guide: Worked example 1; Practice Q3)
- I can judge a claim about the size of a difference by checking whether that value is inside the interval. (Guide: Worked example 1; Practice Q5)
- I can explain how the confidence level, and random sampling or random assignment, affect the conclusion. (Guide: Worked examples 2 and 3; Practice Q4, Q6)
All ticked? Move on to Topic 3.12, Setting Up a Test for the Difference Between Two Population Proportions, or return to the course roadmap.