Week 9 · Suggested 90 minutes · First-pass draft
From observed counts to a statistical test
Use exact and asymptotic reference models, and explain what their p-values do not mean.
Applied assignment, not a stored grade. Instructions and model checks are provided for self-study or instructor adaptation. Work is not transmitted to this site.
What you will do
- Analyze 18 heads out of 20 independent fair-coin trials using the exact binomial test.
- Compute Pearson's goodness-of-fit X² for six observed die-face counts [15,5,10,10,10,10].
- Use the fictional 2-by-2 commuter table to compute expected counts and a chi-square independence statistic.
- For each test, state the null model, relevant test assumptions, statistic, and one interpretation limitation.
What to submit
Three worked tests in a reproducible R script or fully explained calculations.
Self-check before finishing
Two-sided exact coin p ≈ .00040245; die goodness-of-fit X²=5; commuter table X²≈3.516.
Assigned reading
Explain p-values and compare observed to expected category counts.
- Lesson 28: hypothesis tests and p values
- Lesson 29: chi square goodness of fit
- Lesson 30: chi square independence
Instructor discussion guidance
Do not give full credit for writing 'the null is 0.03 likely to be true' or implying that association proves causation.
Print a predict–experiment–explain worksheet → · Open browser R →