Title: Week 10 Overview — Start Here
Course: Introduction to Statistics (18-Week Generic Edition)

Welcome to Week 10: Sampling Distributions & the Central Limit Theorem

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.

The midterm is behind you — welcome to the second half of the course. Weeks 1–8 taught you to get data honestly, describe it, quantify chance, and model it with the bell curve. From here on, one question drives everything: what can a sample really tell us about the world it came from? This week is the engine room. You'll learn the single most useful fact in statistics — averages behave — and by week's end you'll be able to predict how a sample average you haven't even taken yet will act: its center, its spread (the famous σ/√n), and its shape (the Central Limit Theorem's bell, which shows up whether or not the population has one).

The week's big question

"Every honest sample gives a slightly different answer. So how can any one sample's answer be trusted — and by exactly how much does an average wobble?"

By the end of the week you'll answer questions like: how often would a case of 25 candy bags average over 204 g when one bag does it 31% of the time? Should nine adults worry about an 1,800-lb elevator placard? And when a parcel network's daily on-time rate dips to 75%, is that a crisis — or just sampling noise?

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.

- [ ] Explain sampling variability and the sampling distribution — the pile of a statistic's values across all possible samples — and keep the three distributions straight (population · one sample · all the means).
- [ ] Give the center and spread of x̄'s sampling distribution — centered at μ (unbiased), with standard error σ/√n — and keep SD vs. SE straight: σ is the ruler for individuals; σ/√n is the ruler for averages.
- [ ] State the Central Limit Theorem and its fine print — means go approximately normal whatever the population's shape (n ≥ 30 rule of thumb; any n if the population is normal; always a random sample — the CLT fixes shape, never bias).
- [ ] Compute probabilities for a sample mean — z = (x̄ − μ)/(σ/√n) with the Week 8 z-table — including totals-⟺-means questions like the elevator placard.
- [ ] Do the same for a sample proportion p̂ — center p, SE √(p(1−p)/n), after checking np ≥ 10 and n(1 − p) ≥ 10.

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 10 — the module's primary reading; the friendly z-table rides again in its Section 4 | Chapter (ungraded prep) | Early in the week
2 | Skim the slides (Deck 10) and the Week 10 lecture outline; browse the Readings & Resources links that interest you (the StatKey interactive is five minutes well spent) | Prep (ungraded) | Alongside class
3 | Lecture Tutorial 10 — work the week's ideas with your chatbot (it gets the z-table and every worked example), then submit the share link + Completion Summary | Tutorial · graded (Lecture tutorials, 20% group) | End of Week 10
4 | Practice exercises — quick reps with the AI coach | Practice · ungraded | Before the quiz (recommended)
5 | Data Lab 10 — "The Averages Machine: Build a Sampling Distribution by Hand" — draw 30 random penguin samples, bank 30 means, and watch a bell emerge from data that has no bell in it | Data lab · graded (Data labs, 15% group) | End of Week 10
6 | Quiz 10 — sampling distributions, the standard error, the CLT, probabilities for x̄ and p̂ | Quiz · graded (Quizzes, 15% group) · closed to AI | End of Week 10
7 | Discussion 10 — "The Fine Print on 'Average'" — interrogate a real average-based promise with your chatbot as sparring partner; 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 10
8 | Assignment 10 — "Delivery, on Average" — four AI-coached problems at a parcel carrier; submit the report (score on line 1) + chat link | Assignment · graded (Assignments, 25% group) | End of Week 10

Heads-up on the AI work: in this course the chatbot drafts, and you judge. This week's signature catches: chatbots conflating SD and SE, claiming a big sample's histogram "goes normal" (it mirrors the population — only the pile of sample MEANS earns the bell), and dividing by √30 instead of √10 when 30 is the number of samples and 10 is the sample size. The tutorial, lab, and assignment all set you up to 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

- Ask "one value, or an average?" before every formula. That single question picks the right ruler: σ for one value, σ/√n for an average. The wrong-ruler error is the week's (and the half's) most expensive mistake.
- Memorize the two rulers as a sentence, not symbols. "σ is the ruler for individuals; σ/√n is the ruler for averages." Then say your answer in words — "a case average typically strays about 1.6 g" — words catch what symbols hide.
- Respect the √n. Quadruple the sample to halve the noise. (Doubling only buys you 1.41.)
- Keep n and the number of samples separate. In the lab you take 30 samples of n = 10 — the formulas only ever use the 10.
- Say the CLT's full subject out loud. Not "big samples go normal" — "the sampling distribution of the sample mean goes normal." Half the quiz's distractors live in that gap.

You've already built everything this week runs on: the SD from Week 3 and the z-table from Week 8. This week they combine into the engine of inference — come ready to crank it by hand.