Course: Introduction to Statistics (18-week generic edition)
Module: Week 13 of 18 · planned around two ~75-minute sessions
Objective covered: Objective 7 — Carry out and interpret hypothesis tests (this week: the logic — hypotheses, p-values, α, and error types).

This file holds two pieces: (A) the Module 13 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. All timing is relative — "start of Week 13," "end of Week 13" — and maps onto real dates when the adopting instructor sets the term calendar.

(A) Module 13 Overview — Start Here

Welcome to Week 13: Hypothesis Testing — Foundations

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 ended the confidence-interval story: from one sample, a whole range of plausible values. This week flips the question around. Somebody hands you one specific claim — "500 grams per box." "90% on time." "Charges in 90 minutes." — and your data disagree a little. They always do; samples wobble. So which is it: the claim is wrong, or chance did it? Hypothesis testing is the machinery for deciding — the most used, most misused tool in applied statistics. There are no new formulas this week: every p-value is handed to you. The entire week is judgment — and judgment is the part people get wrong.

The week's big question

"A claim says one thing; your data say another. How surprising does the data have to be before you're allowed to call the claim wrong?"

By the end of the week you'll run every claim through the same courtroom: the claim gets the benefit of the doubt (H₀), the data are the evidence, the p-value measures how well plain chance could fake that evidence — and the verdict comes with exact language about what it does and doesn't prove.

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.

• [ ] Write the two hypotheses for any claim — H₀ (the claim as stated, holding the equals sign, about μ or p — never x̄ or p̂) and Hₐ (the suspicion, pointing <, >, or ≠).
• [ ] Say what a p-value means in one sentence — the probability, assuming H₀ is true, of data at least as extreme as yours — and catch the classic misread (it is never the chance the claim is true).
• [ ] Deliver the verdict — compare p to the pre-chosen α (p ≤ α → reject; p > α → fail to reject) and state it with the course's template sentences, in context.
• [ ] Describe both error types in context — Type I (the false alarm, probability α) and Type II (the miss) — and explain why tightening one loosens the other.
• [ ] Separate "significant" from "important" — explain why a huge study can make a trivial effect statistically significant, and why "fail to reject" never means "proven true."

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 judging is specific: chatbots asked to "explain" a test result routinely endorse the p-value misread ("p = 0.21 means a 21% chance the claim is true" — it doesn't) and let "we accept the null" slide. The lab and tutorial both make you catch exactly these.

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

• Learn the courtroom, and everything follows. H₀ is the defendant with the benefit of the doubt; the data are the evidence; α is the standard of proof; the verdict is "guilty" or "not enough evidence" — never "proven innocent."
• Memorize the p-value sentence. The probability, assuming H₀ is true, of data at least as extreme as mine. Every quiz distractor this week is a broken version of that sentence.
• Use the template verdicts. "We reject H₀ — convincing evidence that [Hₐ in context]" / "We fail to reject H₀ — not convincing evidence that [Hₐ in context]." The banned words: accept, proven, true.
• Keep the two errors straight with the wolf. Type I cries wolf when there's no wolf (false alarm, probability α); Type II sleeps through the real one (miss). Tightening one loosens the other.
• Ask "how big?" right after "how surprising?" A p-value measures surprise, not size — 80,000 runners can make 4 meaningless seconds "significant."

You already know more than you think: Week 10 taught you how samples wobble, and Weeks 11–12 taught you to measure the wobble. This week just turns that wobble-knowledge into verdicts. Come to the first session ready to argue about a tea taster.

(B) Welcome Announcement — Module 13

Release setting: drips at the start of Week 13 (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 13."

Subject: Week 13 — the claim is on trial

Hi everyone,

Quick scene: Cambridge, the 1920s, afternoon tea. A scientist claims she can taste whether the milk or the tea was poured into the cup first. A statistician at the table doesn't believe her — so he pours eight cups and invents the modern hypothesis test on the spot. She goes eight for eight. Guessing does that about once in seventy tries. Was she guessing?

This week — Hypothesis Testing: Foundations — we build that exact logic: put a claim on trial (the null hypothesis gets the benefit of the doubt), measure how well plain chance could fake your evidence (the p-value), and deliver a verdict with honest language about what it does and doesn't prove. No new formulas — every p-value is handed to you this week. It's all judgment, which is exactly where headlines, ads, and chatbots go wrong.

Three things not to miss:
1. Chapter 13 is your primary reading — the tea story, the courtroom, and the two ways every verdict can be wrong. Start there.
2. Data Lab 13 has you build the null hypothesis with your own hands: 200 sets of 20 coin flips, then you locate a street performer's suspicious 15-of-20 inside your own chance-world. Due at the end of Week 13.
3. Discussion 13 ("The 0.05 Question") puts a claim from your life on trial — initial post two days before the week ends, so classmates have time to reply.

Callback: last week you built confidence intervals — the range of plausible values. A hypothesis test is the same engine pointed at one specific claimed value: is it plausible? Next week the two ideas formally meet, and you'll compute the tests yourself.

Open the Start Here / Module Overview page first — it lays out everything in order with due points. Bring your skepticism (and an opinion about whether eight-for-eight could be luck) to the first session.

See you in the course!