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 using s in place of σ leads to a t-distribution instead of the standard normal. (Guide: “Why a new distribution?”; Practice Q7(a))
- I can describe t-distributions: symmetric, bell-shaped, heavier tails than the standard normal, and closer to it as df increases. (Guide: “t-distributions”; Practice Q1)
- I can explain why a matched-pairs design is analysed as one sample of differences. (Guide: “Choosing the procedure and defining the parameter”; Practice Q6(a))
Skills
- I can choose a one-sample t-interval for μ or for μd, and tell it apart from a two-sample or proportion procedure. (Guide: Worked example 2; Practice Q3)
- I can define the parameter in context, with the variable, units, population and, for pairs, the order of subtraction. (Practice Q5(a), Q6(b))
- I can find t* for a given confidence level using df = n − 1. (Guide: “The calculation”; Practice Q2)
- I can calculate the standard error s/√n and the margin of error t* × s/√n. (Guide: Worked example 3; Practice Q4)
- I can construct a t-interval from raw data or from summary statistics, keeping unrounded values until the end. (Guide: Worked examples 1 and 3; Practice Q4, Q5)
Reasoning
- I can check the randomization, 10% and sample data conditions with numbers and context, looking at the data when n < 30. (Guide: “The three conditions”; Practice Q5(b))
- I can check the sample data condition on the differences for paired data. (Guide: Worked example 2; Practice Q6(c))
- I can explain what goes wrong if z* is used with s, or if a sample with an outlier is used when n < 30. (Practice Q7)
All ticked? Move on to Topic 4.3, Justifying a Claim Based on a Confidence Interval for a Population Mean or Population Mean Difference, or return to the course roadmap.