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 one calculated interval may or may not contain the population proportion. (Guide: “What a confidence interval does and does not tell you”; Figure 1)
- I can explain why “there is a 95% probability that p is in this interval” is wrong. (Guide: Worked example 3; Practice Q7)
- I can explain why a plausible value is not a proved value. (Guide: “Using an interval to justify a claim”; Practice Q4)
Skills
- I can interpret a confidence interval in context, naming the confidence level, both endpoints, the proportion, the response and the population. (Guide: “Interpreting the interval”; Practice Q5)
- I can interpret a confidence level as the long-run capture rate in repeated random samples of the same size. (Guide: “Interpreting the confidence level”; Practice Q1, Q7)
- I can predict how raising or lowering the confidence level changes z*, the margin of error and the width. (Guide: Worked example 2; Practice Q2)
- I can predict how changing the sample size changes the standard error and the width, using the 1/√n rule. (Guide: Worked example 2; Practice Q3)
- I can tell which of two intervals from the same data has the higher confidence level. (Practice Q6)
Reasoning
- I can decide whether an interval gives convincing evidence for or against a claimed value, using inside or outside. (Guide: Worked example 1; Practice Q4)
- I can judge a directional claim, such as “a majority”, by checking where the whole interval lies. (Guide: Worked example 1; Practice Q5)
- I can explain why the same data can support different conclusions at different confidence levels. (Guide: Figure 2; Practice Q6)
All ticked? Move on to Topic 3.5, Setting Up a Test for a Population Proportion, or return to the course roadmap.