An empirical question you can actually answer
Choose a consequential empirical claim and translate it into a study that could generate evidence, not merely a questionnaire that confirms what you already believe.
Fourteen weeks · Applied statistical reasoning
Do the statistics. Explain them.
The homework builds a scientific argument from data. Each week requires a prediction, calculation or investigation, and a defensible explanation of the limits.
Working coursework: These are complete first-pass prompts for fourteen weeks. They are not calibrated for a particular class's workload or a credential-granting institution; instructor review is still required.
The distribution hiding behind an average
Using the synthetic waiting times from the bootstrap lesson, produce a responsible descriptive statistical report and explain what the long tail changes.
A survey with a moving denominator
Learn why large response counts cannot rescue a population estimate when groups respond at very different rates.
How many ways could the event occur?
Connect enumeration, mutually exclusive events, independent trials, and conditional probabilities.
Rare events and the base-rate trap
Compare what a classifier promises with what a positive result actually means, then connect counts to Poisson assumptions.
What the central limit theorem actually says
Distinguish raw observations from their averages using repeated simulation.
Two kinds of interval, two kinds of uncertainty
Estimate a normal population mean and a binomial proportion without confusing procedure coverage with parameter probability.
What do two groups tell us?
Choose between independent, paired, and binary-outcome comparisons based on design.
From observed counts to a statistical test
Use exact and asymptotic reference models, and explain what their p-values do not mean.
The danger of a beautiful small p-value
Design a study based on a meaningful effect, then evaluate what happens when many hypotheses are tested.
An exact test and a computational interval
Demonstrate two inferential ideas that can be understood without memorizing a reference-distribution table.
Confounding and regression in the same room
Use a historical Simpson's-paradox example and a synthetic regression to separate descriptive patterns from causal claims.
More than one predictor or group
See where an omnibus ANOVA, logistic regression, and a missing-data audit differ from ordinary straight-line fitting.
A research report that can survive scrutiny
Complete the final reproducible statistical investigation and demonstrate that you can communicate uncertainty, data provenance, and limitations.
Four unit self-check assessments → · Final research capstone →