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 tell apart the distribution of a population, the distribution of one sample and the sampling distribution of p̂. (Guide: “Why sample proportions vary”)
- I can explain why μp̂ = p shows that p̂ is an unbiased estimator of p. (Guide: “Mean and standard deviation of p̂”)
- I can say what each condition is for: random and 10% for independence and the standard deviation formula, large counts for the normal shape. (Guide: “The conditions and what each one is for”; Practice Q5(c))
- I can explain how the standard deviation of p̂ changes when the sample size is multiplied by 4. (Guide: Worked example 3; Practice Q2)
Calculation
- I can calculate μp̂ = p and σp̂ = √(p(1 − p)/n). (Guide: Worked example 1; Practice Q1, Q5(a))
- I can check the random, 10% and large-counts conditions with numbers from the context. (Guide: Worked example 1; Practice Q3, Q4(a))
- I can find a probability about p̂ by standardising and using the normal distribution. (Guide: Worked example 2; Practice Q4, Q6(c))
- I can find the smallest sample size that makes σp̂ no larger than a target, rounding up. (Guide: Worked example 3; Practice Q7(a))
Reasoning
- I can interpret the mean and standard deviation of p̂ in context, naming the population and the sample size. (Guide: Worked example 1; Practice Q5(b))
- I can use a probability from the sampling distribution to judge whether a sample result gives reason to doubt a claim, without saying the claim is proved false. (Guide: Worked example 2; Practice Q6(d))
- I can recognise when a normal model is not appropriate because the expected counts are too small. (Guide: “When the large-counts condition fails”; Practice Q3)
All ticked? Move on to Topic 3.3, Constructing a Confidence Interval for a Population Proportion, or return to the course roadmap.