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 the test pools the two samples, using the assumption that H₀: p₁ = p₂ is true. (Guide: “The pooled proportion”; Practice Q7)
- I can explain why the pooled proportion is not the simple average of p̂₁ and p̂₂ when the sample sizes differ. (Guide: “The pooled proportion”; Practice Q1)
- I can explain that z is approximately standard normal when H₀ is true and the conditions are met. (Guide: “The test statistic”)
- I can explain what a randomized experiment lets me conclude that independent random samples do not. (Guide: Worked example 2; Practice Q6)
Skills
- I can calculate p̂₁, p̂₂ and the pooled proportion p̂c from counts. (Practice Q1, Q4)
- I can calculate the two-sample z statistic with the pooled standard error, showing my substitution. (Guide: Worked example 1; Practice Q4)
- I can find the p-value for a left-tailed, right-tailed or two-sided alternative. (Guide: “Finding the p-value”; Practice Q2)
- I can say how z and the p-value change if the groups are numbered the other way round. (Practice Q6)
Reasoning
- I can interpret a p-value in context, stating that it assumes the true proportions are equal. (Guide: “Interpreting the p-value”; Practice Q3, Q6)
- I can make a decision by comparing the p-value with α, using both numbers. (Guide: “Decision and conclusion”; Practice Q5)
- I can write a non-definitive conclusion about the true proportions in context, in terms of Hₐ, and use it to answer the investigative question. (Guide: both worked examples; Practice Q5)
- I can find and correct errors in someone else’s test, such as an unpooled standard error or “accept H₀”. (Practice Q7)
All ticked? Move on to Topic 3.14, Setting Up a Chi-Square Test for Homogeneity or Independence, or return to the course roadmap.