Week 11 — Module Framing · Confidence Intervals for a Mean
Course: Introduction to Statistics (18-week generic edition)
Module: Week 11 of 18 · planned around two ~75-minute sessions
Objective covered: Objective 6 — construct and interpret confidence intervals for a population mean.
This file holds two pieces: (A) the Module 11 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. All timing is relative — "start of Week 11," "end of Week 11" — and maps onto real dates when the adopting instructor sets the term calendar.
(A) Module 11 Overview — Start Here
Welcome to Week 11: Confidence Intervals for a Mean
This is your home base for the week. Read it first, then work the checklist below from top to bottom. Everything you need is linked inside the module.
Last week you learned the engine of inference: sample means wobble around the truth by a knowable amount (the standard error). This week the engine finally drives somewhere. Every "average" you've ever been quoted — your app's 6.9 hours of sleep, a spec sheet's 10-hour battery — was one sample's guess dressed up as the truth: a point estimate, and almost surely not exactly right. The honest alternative is this week's skill: the confidence interval — the guess ± a margin of error, with a stated confidence level. One number is a bluff; a range with a confidence attached is an estimate you can defend.
The week's big question
"A sample gives one number — but the truth is a number we'll never see. How do we turn one honest sample into a range we can defend, with a confidence we can state?"
By the end of the week you'll answer questions like: what range of true average battery lives is plausible from 16 tested laptops? Is a café's "355 mL" label consistent with 16 measured pours? And the deep one — what exactly does "95% confident" promise, and what does it not?
By the end of this week, you can…
Use this as a checklist. If you can do all five out loud, you're ready for the quiz.
- [ ] Name the point estimate for a mean (x̄) — and say why a bare point estimate is almost surely wrong.
- [ ] Explain why t replaces z when σ is unknown, and find df = n − 1 and t* on the friendly t-table ("t is z with humility").
- [ ] Build a one-sample t-interval — conditions, SE = s/√n, ME = t* × SE, then x̄ ± ME — and say it in words, about the mean.
- [ ] Take a margin of error apart — predict what confidence level, n, and s each do to the width (certainty costs width; halving a margin costs 4× the sample).
- [ ] Interpret the interval correctly — the 95% is the method's capture rate (19 tickets in 20) — and catch the two classic misreads: "95% of individuals" and "95% chance μ is in there."
What to do this week, in order
The table below lists the week's items in working order, with what each is worth and when it's due.
| # | Do this | Type | Due |
|---|---|---|---|
| 1 | Read Chapter 11 — the module's primary reading; the friendly t-table lives in its Section 2 | Chapter (ungraded prep) | Early in the week |
| 2 | Skim the slides (Deck 11) and the Week 11 lecture outline; browse the Readings & Resources links that interest you | Prep (ungraded) | Alongside class |
| 3 | Lecture Tutorial 11 — work the week's ideas with your chatbot (it gets the t-table too), then submit the share link + Completion Summary | Tutorial · graded (Lecture tutorials, 20% group) | End of Week 11 |
| 4 | Practice exercises — quick reps with the AI coach | Practice · ungraded | Before the quiz (recommended) |
| 5 | Data Lab 11 — "Ten Penguins and the Truth" — draw your own 10 penguins, build a real 95% interval, and see whether it captures the knowable full-data mean | Data lab · graded (Data labs, 15% group) | End of Week 11 |
| 6 | Quiz 11 — point estimates, t and df, building intervals, margin anatomy, interpretation | Quiz · graded (Quizzes, 15% group) · closed to AI | End of Week 11 |
| 7 | Discussion 11 — "The Single-Number Bluff" — argue whether the world should quote ranges instead of numbers; post the AI summary + chat link | Discussion · graded (Discussions, 15% group) | Initial post two days before week's end; replies by end of Week 11 |
| 8 | Assignment 11 — "Trust, With Margins" — four AI-coached problems (laptops, firefighters' sleep, checkout times, a café label); submit the report (score on line 1) + chat link | Assignment · graded (Assignments, 25% group) | End of Week 11 |
Heads-up on the AI work: in this course the chatbot drafts, and you judge. This week's signature catch: ask a chatbot for a small-sample interval and it will happily use z* = 1.96 where the honest multiplier is t* = 2.262 — an interval ~13% too narrow, faking certainty. Your tutorial, lab, and assignment all embed the course's friendly t-table precisely so you can check the machine against it.
Late policy reminder: 10% off per day late. If life happens, reach out to your instructor before the deadline — early is always easier.
How to succeed this week
- Memorize the recipe as four beats. Conditions → SE = s/√n → ME = t* × SE → x̄ ± ME. Then say it in words, about the mean. Every problem this week is those four beats.
- Say "n minus one" out loud. df = n − 1 — the n = 16 row is 15. The df slip is the week's cheapest lost point.
- Keep SD and SE apart. s is how much individuals spread; s/√n is how much the mean wobbles. A person-sized margin from 25 data points means you used the wrong one.
- Round only at the end. Carry full digits through ME; round the endpoints and say so ("≈ 0.41"). Early rounding makes endpoints that don't reconcile.
- Rehearse the one licensed sentence. "We are 95% confident the mean [X] of all [population] is between [low] and [high]" — and know that the 95% describes the method: 19 intervals in 20 capture the truth, and nobody gets to peek.
You've already built everything this week needs: the SD ruler from Week 3 and the SE engine from Week 10. This week they snap together into the first real tool of inference — come ready to put honest error bars on the world.
(B) Welcome Announcement — Module 11
Release setting: drips at the start of Week 11 (offset = 0 days from module start) — not before. If your platform won't preserve the scheduled release on import, post it as a draft labeled "Release: start of Week 11."
Subject: Week 11 — one number is a bluff (let's build honest ranges)
Hi everyone,
Quick question: your sleep app says you average 6.9 hours a night. Two decimal places, total confidence. How wrong could it be? It watched a sample of your nights — and last week you learned exactly what sample answers do: they wobble. This week we stop bluffing with single numbers. You'll learn to report the honest version — a confidence interval: the guess, plus or minus a margin, with a confidence you can state and defend.
Three things not to miss:
1. Chapter 11 is your primary reading — it carries the friendly t-table the entire week runs on (three rows, three confidence levels; every problem lands exactly on it). Start there.
2. Data Lab 11 is the term's best two minutes of statistics: everyone draws 10 random penguins and builds a real 95% interval around a knowable truth — then we see whether about 95% of the room captured it. Someone will hold a perfectly-built interval that misses. That's not failure; that's the definition of "95% confident," live. The Discussion ("The Single-Number Bluff") wants your initial post two days before the week ends.
3. Catch your chatbot this week. Ask it for a small-sample interval and odds are it grabs 1.96 where the honest multiplier is 2.262. Your tutorial and lab embed the course's t-table so you can check the machine — the tool drafts, you judge.
One habit to bring: after every interval you build, say the sentence — "we are 95% confident the mean … of all …". The two words "mean" and "all" are where the points (and the honesty) live.
Open the Start Here / Module Overview page first — it lays out everything in order with due points. See you in the course!