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 when two samples are independent and when the data are paired, and choose the right interval for each. (Guide: Step 1 and Worked example 3; Practice Q1)
- I can explain why the critical value comes from a t-distribution, not the normal distribution. (Guide: Step 3; Practice Q7)
- I can explain what each of the three conditions protects. (Guide: Step 2)
- I can explain why the 10% condition is not checked in a randomized experiment. (Guide: Worked example 2; Practice Q6)
Skills
- I can define μ₁ − μ₂ in context, with the order of subtraction, the response variable and both populations or treatments. (Guide: Worked examples 1 and 2; Practice Q5, Q6)
- I can check the randomization, 10% and sample data conditions for both groups. (Guide: Step 2; Practice Q3, Q5)
- I can check small samples for strong skewness and outliers using a dot plot or the 1.5 × IQR rule. (Guide: Worked example 2; Practice Q6)
- I can calculate the standard error √(s₁²/n₁ + s₂²/n₂) without adding standard deviations. (Practice Q2, Q4)
- I can find t* with technology df or with the conservative df, and state which I used. (Guide: Step 3; Practice Q4)
- I can calculate the margin of error and the interval, with units. (Guide: Worked example 1; Practice Q4, Q5)
Reasoning
- I can say why a conservative df gives a slightly wider interval and why n₁ + n₂ − 2 is not conservative. (Practice Q7)
- I can explain why large samples (both n ≥ 30) make skewed sample data acceptable. (Practice Q5)
- I can find and correct errors in someone else’s two-sample interval. (Practice Q7)
All ticked? Move on to Topic 4.8, Justifying a Claim Based on a Confidence Interval for the Difference Between Two Population Means, or return to the course roadmap.