Course: Introduction to Statistics (18-week generic edition)
Module: Week 15 of 18 · planned around two ~75-minute sessions
Objective covered: Objective 7 — Conduct and interpret hypothesis tests for proportions and two-sample comparisons, and choose the right procedure.

This file holds two pieces: (A) the Module 15 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. All timing is relative — "start of Week 15," "end of Week 15" — and maps onto real dates when the adopting instructor sets the term calendar.

(A) Module 15 Overview — Start Here

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.

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.

(B) Welcome Announcement — Module 15

Release setting: drips at the start of Week 15 (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 15."

Subject: Week 15 — you're in an experiment right now

Hi everyone,

Quick claim before we start: sometime this week, an app will experiment on you. One version of a screen for you, another for someone else, a counter ticking in the background. Nobody will ask. The tech world calls it an A/B test — and by the end of this week, you'll know the exact statistics behind it, because it's this course's machinery pointed at two groups at once.

This week — Testing Proportions & Two-Sample Inference — closes the everyday testing toolbox: the one-proportion z-test (is a claimed percentage true?), the two-proportion z-test and the two-sample t-test (do two groups really differ?), and the map for picking the right tool on sight. Last week you put means on trial; this week percentages and pairs of groups take the stand.

Three things not to miss:
1. Chapter 15 is your primary reading — it re-prints the friendly z-table and carries every worked example the week leans on. Start there.
2. Data Lab 15 — "Split the Traffic" — you'll rig two checkout pages where YOU know the truth, simulate 400 shoppers, and watch the test catch the difference… most of the time. The runs that miss are the whole lesson. Due at the end of Week 15.
3. Discussion 15 — "The Everyday A/B Test" wants your initial post two days before the week ends — come argue about whether silent experiments on users need consent, and when a "significant" win should actually ship.

One heads-up for the AI work: this week your chatbot will confidently tell you that a non-significant result means "the groups are the same." In the lab, you'll know the truth and it won't — catching that mistake is graded. The tool drafts; you judge.

Next stop after this: categorical data get a test of their own (chi-square), and then the story wraps. The toolbox is nearly full — come get its two most-used tools.

See you in the course!