Title: Week 14 Overview — Start Here
Course: Introduction to Statistics (18-Week Generic Edition)

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.

# | Do this | Type | Due
1 | Read Chapter 14 — the module's primary reading (the course t-table is inside) | Chapter (ungraded prep) | Early in the week
2 | Skim the slides (Deck 14) and the Week 14 lecture outline; browse the Readings & Resources links that interest you | Prep (ungraded) | Alongside class
3 | Lecture Tutorial 14 — work the t-test machinery with your chatbot, then submit the share link + Completion Summary | Tutorial · graded (Lecture tutorials, 20% group) | End of Week 14
4 | Practice exercises — quick reps with the AI coach | Practice · ungraded | Before the quiz (recommended)
5 | Data Lab 14 — "Put the Field Guide on Trial" — your own random penguin sample tests a reference value; about 1 classmate in 20 should convict an innocent claim | Data lab · graded (Data labs, 15% group) | End of Week 14
6 | Quiz 14 — hypotheses, t-statistics, verdicts, tails, paired data, the duality | Quiz · graded (Quizzes, 15% group) · closed to AI | End of Week 14
7 | Discussion 14 — "The 'On Average' Alibi" — when a claim survives the test, may the company say "confirmed"? Post the AI summary + chat link | Discussion · graded (Discussions, 15% group) | Initial post two days before week's end; replies by end of Week 14
8 | Assignment 14 — "Claims on Trial" — four AI-coached problems; submit the report (score on line 1) + chat link | Assignment · graded (Assignments, 25% group) | End of Week 14

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.