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 what an expected count represents: the count I would expect in a cell if H₀ were true. (Guide: “Expected counts”)
- I can explain why χ² is never negative and why larger values give stronger evidence against H₀. (Guide: “The chi-square statistic”; Practice Q7)
- I can explain why the p-value for a chi-square test is always a right-tail area. (Guide: “Finding the p-value”; Practice Q2, Q7)
- I can explain why failing to reject H₀ does not show that two variables are independent or that distributions are the same. (Guide: Worked example 2; Practice Q7)
Skills
- I can calculate every expected count with (row total × column total) ÷ table total and check that the expected counts add to the observed totals. (Guide: Worked example 1; Practice Q1, Q4)
- I can calculate each component and add them to get χ², using counts, not percentages. (Guide: Worked example 1; Practice Q4)
- I can find the degrees of freedom as (rows − 1)(columns − 1). (Guide: “Degrees of freedom and the null distribution”; Practice Q2)
- I can find the p-value with technology, or a range for it from a chi-square table. (Guide: “Finding the p-value”; Practice Q2, Q4)
Reasoning
- I can interpret the p-value in context, starting with “Assuming [H₀ in context]…”. (Guide: “Interpreting the p-value”; Practice Q3, Q6)
- I can make a decision by comparing the p-value with a pre-chosen α, quoting both numbers. (Guide: “Decision and conclusion”; Practice Q5, Q6)
- I can write a non-definitive conclusion in terms of Hₐ that names the population(s), with the correct wording for homogeneity or independence. (Guide: Worked examples 1 and 2; Practice Q5, Q6)
- I can use the test result to answer the investigative question that started the study. (Guide: Worked examples 1 and 2)
All ticked? Unit 3 is complete. Move on to Topic 4.1, Sampling Distributions for Sample Means, or return to the course roadmap.