Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Module: Week 12 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 6 — Construct and interpret confidence intervals for proportions.

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. Dates below assume a Tuesday/Thursday session pattern with Week 12 meeting Tue Nov 17 and Thu Nov 19, and end-of-week work due Sunday Nov 22, 11:59 p.m. Note: this is the last full week before Thanksgiving break (campus closed Thu–Fri, Nov 26–27) — everything is due before the break. Adjust the day-of-week and times to match your section.

(A) Module 12 Overview — Start Here

Welcome to Week 12: Confidence Intervals for Proportions

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, we built an honest range — a confidence interval — for a population mean using the t-distribution. This week is the version you actually see most often in the news: the interval for a percentage. "45% approve, ±4 points" is a confidence interval for a proportion, and by Friday you'll build one yourself, choose the sample size behind a target margin, and say exactly what the interval means without the two errors almost everyone makes.

Campus note: This is the last full week before Thanksgiving break (campus closed Thu–Fri, Nov 26–27). Our Tuesday and Thursday sessions run normally, and everything is due Sunday, Nov 22 — comfortably before anyone travels.

The week's big question

"Where does '±4 points' come from when the data is a percentage, not an average — and how do pollsters choose a sample size to hit a target margin?"

By Friday you'll be able to take a poll's percentage and sample size — say 40% of 600 people — and build an interval like (0.361, 0.439), and flip it around to tell a pollster how many people they must survey for a target margin.

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.

• [ ] Check the three conditions for a one-proportion z-interval — random, independent, and large counts (n·p̂ ≥ 10 and n(1−p̂) ≥ 10).
• [ ] Construct a confidence interval for a proportion as p̂ ± z*·√(p̂(1−p̂)/n) — using the z* value we supply (no table lookups), and remembering proportions use z*, not t (no degrees of freedom).
• [ ] Compute and describe the margin of error (ME = z*·√(p̂(1−p̂)/n)) and say what makes it bigger or smaller.
• [ ] Choose a sample size for a target margin of error with n = (z*/ME)²·p̂(1−p̂), using the worst-case p̂ = 0.5 when you have no estimate, and rounding up.
• [ ] Interpret a proportion interval correctly and catch the two classic misreadings — "95% of people" and "95% chance the true proportion is in THIS interval."

What's due this week, and when

Work these in order — each one gets you ready for the next.

Heads-up on the AI tutorial: you'll use a chatbot to draft, and then you judge its work against what we cover in class. Chatbots routinely botch this — they'll say "there's a 95% probability the true proportion is in this interval" (it's the method that's 95% reliable) or "95% of people are within 4 points" (a CI is about the overall rate), and they sometimes forget to use p̂ = 0.5 for a worst-case sample size or round up. Catching the model is the point.

Late policy reminder: 10% off per day late. If life happens, reach out before the deadline — I'd much rather hear from you early.

How to succeed this week

• Lead with the idea, not the notation. A confidence interval is just "our best guess, give or take an honest margin." The formula p̂ ± z*·√(p̂(1−p̂)/n) comes after that idea clicks.
• Proportions use z*, not t — and there are no degrees of freedom. That t-with-df machinery was last week's interval for a mean. This week we supply z* directly (90% → 1.645, 95% → 1.960, 99% → 2.576). Your job is to use it, not find it.
• Memorize the four-step build. SE = √(p̂(1−p̂) ÷ n) → z* from our table → ME = z* × SE → interval = p̂ − ME to p̂ + ME.
• Worst case = 0.5. When you size a sample and don't know p̂, plug in 0.5 (it's the largest, safest n) — and always round n up to a whole person.
• Memorize the one correct sentence. "We're 95% confident the true proportion is between ___ and ___." The 95% is about the method over many samples — not the people, and not a coin flip on this one interval.
• Treat the chatbot as a smart intern, not an oracle. It drafts the interpretation; you check it against the two banned sentences. That habit is the whole semester in miniature.

You've already done the hard conceptual lift (sampling distributions, and last week's intervals for a mean). This week just swaps in the proportion formula and adds the pollster's sample-size trick. Come to class ready to argue about a poll's "±4 points." See you Tuesday.

(B) Welcome Announcement — Module 12

Release setting: post on the module's start day (offset = 0 days), i.e., Tue Nov 17, 2026 — not before. If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Tue Nov 17."

Subject: Week 12 — build the "±4 points" you see on every poll 📊

Hi everyone,

Last week we built a "±" for an average. This week we build the one you actually read most often: the "±" on a percentage. "45% approve — margin of error ±4 points" is a confidence interval for a proportion, and by Friday you'll build one yourself — and figure out how many people a pollster has to survey to get a margin that small.

This week — Confidence Intervals for Proportions — we tackle the big question: Where does "±4 points" come from when the data is a percentage, and how do pollsters choose a sample size to hit a target margin? Good news: we supply every z* value you need — no table lookups (and proportions use z*, not last week's t — no degrees of freedom).

A couple of logistics:
- This is the last full week before Thanksgiving break (campus closed Thu–Fri, Nov 26–27). Our Tue/Thu sessions run normally, and everything is due Sun Nov 22 — before you travel.

Three things not to miss:
1. Lecture Tutorial 12 — work through building and interpreting a proportion interval (and sizing a sample) with one approved chatbot (Gemini, Claude, or ChatGPT) and submit the share link. You'll catch the model's interpretation mistakes, not just trust them. Due Sun Nov 22.
2. Quiz 12 and Assignment 12 also close Sun Nov 22 — both lean on the four-step build, the worst-case sample size, and the correct interpretation, so do the tutorial and practice first.
3. Discussion 12 asks you to find a real poll percentage with its margin (a poll's "45%, ±4 points" works great) and reason about what it means and how the sample size drives the margin — initial post Fri Nov 20, replies Sun Nov 22, so start early.

One promise: by the end of this week you'll never again be fooled by the two sentences that get confidence intervals wrong — and you'll understand why national polls so often survey about a thousand people. Open the Start Here / Module Overview page first — it lays out everything in order with due dates. Bring a poll you've seen (and an opinion about whether "±4" is big or small) to class on Tuesday.

See you soon,
Prof. Rivera