Title: Week 15 Overview — Start Here
Course: Introduction to Statistics (18-Week Generic Edition)

Welcome to Week 15: Testing Proportions & Two-Sample Inference

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.

Sometime this week, an app almost certainly ran an experiment on you — one checkout page for you, another for the next visitor, a counter ticking somewhere. That practice is the A/B test, and this week you learn the exact machinery behind it. Week 13 gave you the courtroom logic of testing; Week 14 aimed it at means. This week closes the toolbox: testing a claimed percentage, comparing two groups (rates and averages), and — the skill that ties the whole inference half together — choosing the right procedure on sight.

The week's big question

"Half the internet is a running experiment. How do we test a claim about a percentage — and how do we tell whether two groups really differ or just wobbled apart by chance?"

By the end of the week you'll read every "significantly better" headline differently: you'll know what test sat behind it, whether its design permits the word because, and why "no significant difference" is a shrug, not a verdict.

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.

- [ ] Run a complete one-proportion z-test — hypotheses about p (never p̂), conditions checked with p₀ (np₀ ≥ 10 and n(1 − p₀) ≥ 10), SE from p₀, z, p-value, conclusion in context.
- [ ] Read a two-proportion printout — including why the SE pools (H₀ says "one shared rate," so estimate that one rate from everyone).
- [ ] Read a two-sample t printout — with its technology-reported df — and conclude with the licensed language.
- [ ] Tell paired from independent designs ("could I match each measurement in one group to exactly one in the other?").
- [ ] Choose the right procedure for any study — one-prop z, two-prop z, one-sample t, two-sample t, or paired t — and say which designs earn causal conclusions.

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 15 — the module's primary reading (it re-prints the friendly z-table) | Chapter (ungraded prep) | Early in the week
2 | Skim the slides (Deck 15) and the Week 15 lecture outline; browse the Readings & Resources links that interest you | Prep (ungraded) | Alongside class
3 | Lecture Tutorial 15 — work through the week's ideas with your chatbot, then submit the share link + Completion Summary | Tutorial · graded (Lecture tutorials, 20% group) | End of Week 15
4 | Practice exercises — quick reps with the AI coach | Practice · ungraded | Before the quiz (recommended)
5 | Data Lab 15 — "Split the Traffic: Your Own A/B Test" — rig two checkout pages with different true rates, simulate 400 shoppers, and see whether the test catches the difference you built | Data lab · graded (Data labs, 15% group) | End of Week 15
6 | Quiz 15 — one-prop z, two-prop and two-sample-t printouts, conditions, choosing the procedure | Quiz · graded (Quizzes, 15% group) · closed to AI | End of Week 15
7 | Discussion 15 — "The Everyday A/B Test" — work out your stance on being silently experimented on (and your shipping rule for "significant" wins) with your chatbot, post the AI summary + chat link, then reply to two classmates | Discussion · graded (Discussions, 15% group) | Initial post two days before week's end; replies by end of Week 15
8 | Assignment 15 — "Two Groups Walk Into a Test" — four AI-coached problems; submit the report (score on line 1) + chat link | Assignment · graded (Assignments, 25% group) | End of Week 15

Heads-up on the AI work: in this course the chatbot drafts, and you judge. This week's known chatbot failure modes: skipping the pooled proportion in two-proportion tests, calling a p-value "the chance the groups are equal," and — the big one — declaring that a non-significant run "proves the groups are the same." The data lab is built so you catch that last one red-handed: you'll know the truth, and the AI won't.

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 one line that prevents half the errors: interval → p̂; test → p₀. The test lives in H₀'s world, so the claim supplies the SE and the large-count check.
- Photograph the procedure map (it's one slide and one chapter table): counting successes or measuring amounts? one sample, two samples, or the same individuals twice? Two questions, five tools.
- Say the licensed sentences out loud. "Convincing evidence the rates differ." "The data do not provide convincing evidence of a difference." Never "proves," never "accept H₀."
- Keep significance and importance separate. A tiny p-value answers "is it chance?" — only the size of the difference, in real units, answers "does it matter?"
- Let the lab's misses teach you. About one honest run in five will fail to find a difference you know is there. Carry that into every "study finds no difference" headline you ever read.

You've built every part of this week already — Week 1's random assignment, Week 10's standard errors, Week 13's logic, Week 14's t. This week just snaps the pieces together into the toolset working analysts actually use. Come argue about being experimented on.