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 population distribution, the distribution of one sample and the sampling distribution of x̄. (Guide: “From proportions to means”)
- I can explain why x̄ is an unbiased estimator of μ and why sample means vary less than individual values. (Guide: “Mean and standard deviation of x̄”; Practice Q4)
- I can explain what each condition is for: randomization for independence and no bias, 10% for the standard deviation formula, and population shape or n ≥ 30 for a normal model. (Guide: “The conditions”; Practice Q2, Q6)
- I can explain why a strongly skewed population may need a sample much larger than 30. (Guide: “The conditions”)
Calculation
- I can calculate μx̄ and σx̄ = σ/√n for a given population and sample size. (Guide: Worked example 1; Practice Q1)
- I can find how the sample size must change to reach a target σx̄, and round the answer up. (Guide: Worked example 2(d); Practice Q3)
- I can calculate a normal probability for x̄ by standardising with σ/√n. (Guide: Worked examples 1 and 2; Practice Q4, Q5)
- I can find a cut-off value for x̄ from a probability with invNorm. (Practice Q7(d))
Reasoning
- I can decide, with numbers and context, whether a normal model for x̄ is appropriate, and name the condition that fails if it is not. (Guide: Worked example 2(e); Practice Q6)
- I can interpret μx̄, σx̄ and a probability about x̄ for the specific population and sample size. (Guide: “Interpreting results in context”; Practice Q5(c))
- I can use a small probability about x̄ to explain why a claimed population mean is doubtful, without calling it proof. (Practice Q7(c))
All ticked? Move on to Topic 4.2, Constructing a Confidence Interval for a Population Mean or Population Mean Difference, or return to the course roadmap.