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 the difference between a parameter and a statistic, and say which one is fixed and which one varies from sample to sample. (Guide: “From a sample to a population value”; Practice Q1)
- I can explain the difference between an estimator (the rule) and a point estimate (the number from one sample). (Guide: “Estimator or estimate?”)
- I can state what it means for an estimator to be unbiased, using the centre of its sampling distribution. (Guide: “What makes an estimator unbiased?”; Practice Q2)
- I can explain why an unbiased estimator still gives estimates that miss the parameter. (Guide: Worked example 2)
- I can explain why p̂ and x̄ are unbiased only when the sample is random. (Guide: “What makes an estimator unbiased?”; Practice Q7)
Skills
- I can calculate a point estimate of a proportion, mean, standard deviation or median from sample data. (Guide: Worked example 1; Practice Q4)
- I can use correct notation (p, μ, σ for parameters; p̂, x̄, s for statistics) and describe the parameter in context. (Practice Q1, Q4(c))
- I can list every possible sample from a small population and find the mean of an estimator’s sampling distribution. (Guide: Worked example 2; Practice Q5)
Reasoning
- I can justify whether an estimator is biased or unbiased, and give the direction of any bias, from a complete list of samples. (Guide: Worked example 2; Practice Q5, Q6)
- I can judge from simulation results whether an estimator appears unbiased, allowing for chance variation. (Guide: Worked example 3; Practice Q3)
- I can explain that a larger sample reduces variability but does not remove bias. (Guide: “Bias and variability are different ideas”; Practice Q5(d), Q7)
All ticked? Move on to Topic 3.2, Sampling Distributions for Sample Proportions, or return to the course roadmap.