Course: Introduction to Statistics (18-week generic edition)
Module: Week 14 of 18 · planned around two ~75-minute sessions
Objective covered: Objective 7 — Conduct and interpret hypothesis tests (the means portion: one-sample and paired t procedures).

This file holds two pieces: (A) the Module 14 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. All timing is relative — "start of Week 14," "end of Week 14" — and maps onto real dates when the adopting instructor sets the term calendar.

(A) Module 14 Overview — Start Here

Welcome to Week 14: Testing Claims About Means

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 learned the logic of hypothesis testing — but every p-value was handed to you. This week the training wheels come off. Companies promise averages constantly ("average delivery: 50 minutes," "40 mpg highway"), and an average is a slippery thing to promise, because no single bad experience can contradict it. A sample can. This week you learn to compute the evidence yourself and run the full trial on any claimed average — including the before/after kind, where the same people are measured twice.

The week's big question

"A company promises an average — and your sample disagrees a little. How far from the promise does the data have to drift before 'a little off' becomes 'we don't believe you'?"

The answer is measured the way this course measures everything since Week 10: in standard errors. The week's one-liner: a t-statistic counts standard errors between the data and the claim.

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-sample t-test — hypotheses, conditions, SE = s∕√n, t = (x̄ − μ₀)∕SE, cutoff from the t-table at df = n − 1 — and state the verdict in context.
• [ ] Choose the alternative before the data — two-sided to audit a claim, one-sided only when the direction was the declared question — and explain how the choice changes the cutoff (95% column vs. 90% column).
• [ ] Recognize paired data (same individual measured twice) and analyze it by the week's hook: subtract first — then it's one sample.
• [ ] Use the test ↔ interval duality: a value inside the 95% CI survives the two-sided α = 0.05 test; outside, it's rejected — and the interval's width shows the doubt the bare verdict hides.
• [ ] Say verdicts honestly: "fail to reject" is not guilty, never innocent — and a significant result still needs its effect size reported in real units.

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: chatbots running t-tests commit this week's classic errors constantly — dividing by s instead of s∕√n, sneaking in 1.96 where the t-table says 2.064, or "confirming" a claim after a fail-to-reject. The lab and tutorial both make you catch these. The chatbot drafts; you judge.

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 recipe, not the numbers. Claim → ruler → distance → cutoff → verdict. Every problem this week is those five moves; only the surfaces change.
• Make SE its own line. Nearly every wrong answer this week is one skipped step: t = (x̄ − μ₀)∕SE, with SE = s∕√n computed first. The √n is where your sample size earns its keep.
• Match the table column to the question. Two-sided at α = 0.05 → the 95% column (2.262 / 2.131 / 2.064). One-sided at 5% → the 90% column. And pick your tail before you peek.
• For before/after data, subtract first. Each person is their own control; the t-test runs on the differences, df = pairs − 1.
• Keep Week 11 open. The 95% CI is the list of every claim that would survive this week's two-sided test — if your test and your interval disagree, one of them has an arithmetic error.

You already own every part of this machine — Week 10 built the ruler, Week 11 the table, Week 13 the logic. This week just points them at a promise. Come to the first session with an "on average" claim you've personally stopped believing.

(B) Welcome Announcement — Module 14

Release setting: drips at the start of Week 14 (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 14."

Subject: Week 14 — the promise, the sample, and the verdict

Hi everyone,

Last week you learned the courtroom rules: hypotheses, p-values, and the two verdicts. But every p-value was handed to you. This week you compute the evidence yourself — and aim it at the most common claim in the wild: a promised average.

This week — Testing Claims About Means — the big question: a courier promises "50 minutes on average," your 25 timed deliveries average 52 — broken promise, or sampling noise? By the end of the week you'll settle exactly that with the one-sample t-test, handle before/after data with one clever subtraction, and use Week 11's confidence intervals to see what a verdict quietly leaves open.

Three things not to miss:
1. Chapter 14 is your primary reading — the course t-table (the same one from Week 11) is inside, and everything else this week leans on it.
2. Data Lab 14 — "Put the Field Guide on Trial" — your own random sample of penguins tests a reference value. Here's the fun part: the reference is essentially true, so about one classmate in twenty will convict it anyway. Type I error stops being a definition this week; someone in class will commit one, honestly. Due at the end of Week 14.
3. Discussion 14 — "The 'On Average' Alibi" — when a company's claim survives a test, can it advertise "independent testing confirms our claim"? You'll take a side. Initial post two days before the week ends, so classmates have time to reply.

One habit that will carry you through the week: write the standard error on its own line before you touch anything else. Nearly every wrong t this week is a skipped SE.

Open the Start Here / Module Overview page first — it lays out everything in order with due points. Bring a promise you've stopped believing.

See you in the course!