Course: Introduction to Statistics (18-week generic edition)
Module: Week 12 of 18 · planned around two ~75-minute sessions
Objective covered: Objective 6 — Construct and interpret confidence intervals for a population proportion, and determine the sample size a target margin of error requires.

This file holds two pieces: (A) the Module 12 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. All timing is relative — "start of Week 12," "end of Week 12" — and maps onto real dates when the adopting instructor sets the term calendar.

(A) Module 12 Overview — Start Here

Welcome to Week 12: Confidence Intervals for a Proportion

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 built your first confidence intervals — for a mean, with the t-multiplier. This week the same machine estimates the most public statistic in the world: the percent. Every poll in your feed ends with the same fine print — "margin of error ±3 percentage points" — and by the end of this week that fine print is yours: you'll know where the 3 comes from, you'll recompute it from a real poll's own numbers in the lab, and you'll know the two things it does not protect you from.

The week's big question

"Every poll ends with '±3 points.' Where does that number come from, what does it promise — and what does it quietly leave out?"

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.

• [ ] Compute p̂ and its standard error — SE = √( p̂(1 − p̂) ⁄ n ) — feeding it proportions, never counts.
• [ ] Check the password before building — random sample · at least 10 successes and 10 failures · population at least 10 × n.
• [ ] Build the one-proportion z-interval — p̂ ± z·SE with z = 1.645 / 1.96 / 2.576 — and state the trade-off: surer means wider.
• [ ] Interpret it correctly — "we are 95% confident the interval captures the true proportion" — and spot the two classic misreadings (it's never a 95% chance about one interval, and never about 95% of individuals).
• [ ] Price a survey — n = p(1 − p)(z ⁄ ME)², with p = 0.5 when you know nothing, always rounded up — and audit a media poll's margin of error from its own n.

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.

Heads-up on the AI work: in this course the chatbot drafts, and you judge. This week's classic chatbot fumbles: answering the famous "1,067" for a ±3 sample size instead of rounding 1067.11 up to 1,068, and blessing the sentence "there's a 95% chance the true value is in the interval" (the 95% belongs to the method, not to one interval). Catching these is literally the lab's graded AI-critique step.

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

• Say the chant. Estimate ± multiplier × standard error — "center ± reach." It's the same anatomy as last week; only the fuel changed (means → t, proportions → z).
• Memorize three numbers, not a table. 1.645 (90%) · 1.96 (95%) · 2.576 (99%). Everything else this week is arithmetic.
• Check the password before you build. Random · ≥10 successes and ≥10 failures · population ≥ 10n. A failed condition isn't a technicality — it's the machine telling you the answer would be junk.
• Practice the sentence. Every interpretation needs all three ingredients: the confidence level, the interval, and the population's proportion. If your sentence contains "chance" or "of the people," rebuild it.
• Read whole intervals, not point estimates. 48% ± 3 runs from 45 to 51 — that's "majority undecided," not "the bond fails." This one habit will change how you read the news.

You already own every ingredient this week uses — p̂ from Week 1, the normal curve from Week 8, standard error from Week 10, and interval thinking from Week 11. This is the week they click together in public.

(B) Welcome Announcement — Module 12

Release setting: drips at the start of Week 12 (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 12."

Subject: Week 12 — the fine print at the bottom of every poll is about to be yours

Hi everyone,

Quick experiment: find any poll in your news feed this week. Somewhere near the bottom it says "margin of error ±3 percentage points." You've scrolled past that sentence a hundred times. By the end of this week, you'll be able to recompute it from the article's own numbers — in six spreadsheet cells — and you'll know the two things it quietly doesn't cover.

This week — Confidence Intervals for a Proportion — the machine you built last week gets its most public job. Last week: intervals for a mean, with the t-multiplier. This week: the same estimate ± reach anatomy for percents — renewal rates, recycling rates, return rates, poll numbers — with the z-multiplier and just three numbers to remember (1.645, 1.96, 2.576).

Three things not to miss:
1. Chapter 12 is your primary reading — the whole build lives there, including the z table and the sample-size formula. Start there; everything else gets easier.
2. Data Lab 12 — "Anatomy of a Poll" — you'll audit a real published poll's margin of error (or the provided one) and check whether its fine print survives your recomputation. Due at the end of Week 12.
3. Discussion 12 — "The 400 vs. 18,000 Problem" — a random sample of 400 says 62%; an opt-in app poll of 18,000 says 44%. Which should the city council believe? Initial post is due two days before the week ends*, so classmates have time to reply.

Plus the usual rhythm: Tutorial 12 (your AI tutor — share link + summary), the ungraded practice set, Quiz 12 (closed to AI), and Assignment 12 — "The Honest Percent" (AI-coached, best attempt counts). All due at the end of Week 12.

One heads-up from the future: next week someone walks in with a specific claim — "our support is 60%" — and we test whether it's plausible. The interval you master this week is the doorway to hypothesis testing.

Open the Start Here / Module Overview page first — it lays out everything in order with due points. Bring one poll from your own feed to the first session; we'll put its fine print on trial.

See you in the course!