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 x̄₁ − x̄₂ is an unbiased estimator of μ₁ − μ₂. (Guide: “Mean and standard deviation of x̄₁ − x̄₂”)
- I can explain why the variances add even though the means are subtracted. (Guide: “Mean and standard deviation of x̄₁ − x̄₂”; Practice Q7)
- I can explain why the formula does not apply to paired data from the same individuals. (Guide: “The conditions and what each one is for”; Practice Q2, Q7)
Calculation
- I can calculate the mean and standard deviation of the sampling distribution of x̄₁ − x̄₂, stating the order of subtraction. (Guide: Worked example 1; Practice Q1, Q5)
- I can predict how changing one or both sample sizes changes the standard deviation. (Guide: Worked example 3; Practice Q3, Q7)
- I can turn a statement such as “group 2’s sample mean is larger” into an inequality and find the probability with a normal model. (Guide: Worked examples 1 and 3; Practice Q5)
Reasoning
- I can check the randomization and 10% conditions for two independent samples, and explain why an experiment needs only random assignment. (Guide: Worked example 3; Practice Q5, Q6)
- I can decide whether the sampling distribution is normal (both populations normal) or approximately normal (both samples of at least 30), or neither. (Guide: Worked examples 1 and 2, “When the normal model is not justified”; Practice Q2, Q6)
- I can interpret the mean, standard deviation and a probability in context, naming both populations and the sample sizes. (Guide: Worked examples 1 and 2; Practice Q4, Q5)
- I can use a probability to judge whether an observed difference casts doubt on stated values, without claiming proof. (Guide: Worked example 2; Practice Q6)
All ticked? Move on to Topic 4.7, Constructing a Confidence Interval for the Difference Between Two Population Means, or return to the course roadmap.