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 what the sampling distribution of p̂1 − p̂2 is, and why the difference changes from one pair of samples to the next. (Guide: “Why compare two proportions?”)
- I can explain why p̂1 − p̂2 is an unbiased estimator of p1 − p2. (Guide: “Mean and standard deviation of p̂1 − p̂2”; Practice Q1)
- I can explain why the variances add when the proportions are subtracted, and why the standard deviation of the difference is larger than either one alone. (Guide: “Mean and standard deviation of p̂1 − p̂2”; Practice Q7)
- I can say what each condition is for: randomization and 10% for independence, large counts for the normal shape. (Guide: “The conditions and what each one is for”)
Skills
- I can calculate the mean and standard deviation of p̂1 − p̂2, stating the order of subtraction. (Guide: Worked example 1; Practice Q2, Q4)
- I can check the randomization and 10% conditions for two independent random samples, with numbers from the context. (Guide: Worked example 1; Practice Q5)
- I can check the randomization condition for an experiment and explain why the 10% condition is not needed. (Guide: Worked example 3; Practice Q3, Q6)
- I can check all four expected counts and say when a normal model should not be used. (Guide: “When the large-counts condition fails”; Practice Q3)
- I can turn a statement such as “group 2 is at least as high” into an inequality about p̂1 − p̂2 and find its probability with a normal model. (Guide: Worked example 2; Practice Q5, Q6)
- I can find the smallest equal sample size that gives a required standard deviation. (Practice Q7)
Reasoning
- I can interpret the mean, the standard deviation and a probability for p̂1 − p̂2 in context, naming both populations. (Guide: Worked examples 1 and 2; Practice Q4)
- I can use a probability to judge whether an observed difference is surprising, without claiming proof. (Guide: Worked example 2)
- I can find and correct errors in someone else’s standard deviation calculation. (Practice Q2, Q7)
All ticked? Move on to Topic 3.10, Constructing a Confidence Interval for a Difference in Two Proportions, or return to the course roadmap.