Week 7 · Suggested 90 minutes · First-pass draft
Two kinds of interval, two kinds of uncertainty
Estimate a normal population mean and a binomial proportion without confusing procedure coverage with parameter probability.
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
- For synthetic readings 2,4,6,8,10, calculate the sample mean, sample SD, and 95% Student-t interval.
- For 4 successes among 20 independent trials, compute the 95% Wilson proportion interval.
- Run the known-sigma coverage laboratory and note observed coverage over repeated batches.
- Explain which assumptions differ between the Student-t, Wilson, and known-sigma normal procedures.
What to submit
Two worked intervals with a written comparison and a paragraph explaining frequentist coverage.
Self-check before finishing
The t interval is approximately [2.07,9.93], and the Wilson proportion interval is approximately [0.081,0.416].
Assigned reading
Interpret coverage, t intervals, Wilson score intervals, and data assumptions.
- Lesson 22: confidence intervals
- Lesson 23: one sample t inference
- Lesson 24: confidence intervals for proportions
Instructor discussion guidance
Require identification of the denominator and of the fact that the fixed true parameter is not randomly moving in repeated sampling.
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