Week 18 · Lecture outline

Week 18 — Cumulative Review Outline & Final Administration · Final Exam Week

Introduction to Statistics Generic evergreen edition

Course: Introduction to Statistics (18-week generic edition)
Objectives covered: Objectives 1–9 — the whole course, in review. No new material this week.
SLOs touched: A (reason quantitatively from data) · B (communicate results to a non-technical audience)
Meeting pattern: planned as 2 sessions × ~75 min. Session 1 = the cumulative review (segments below). Session 2 = the final exam (administration notes at the end), closing with a short course send-off.

Week at a Glance


The week's job	Consolidate Weeks 1–17 into one working toolkit, rehearse under exam-like conditions, then take the final — a low-stakes checkpoint worth 5%.
The final	60 auto-graded questions × 2 points = 120 points · cumulative (about 24 questions from Weeks 1–8, about 36 from Weeks 10–17) · closed to AI · sits mid-week so the last days stay free.
The exam bundle	Study guide (M) → practice exam (O, unlimited attempts, ungraded) → exam-prep tutorial (N, graded share-link submission) → the final (L). Work them in that order.
Key message to students	The grade has lived in the weekly work all term; the final is 5%. It is a mirror, not a cliff. Preparation this week is about consolidating, not cramming.
Materials	review deck (Deck 18), the Week 18 study guide, the three embedded tables (z, t, chi-square) students have used since Weeks 8/11/16, a spreadsheet for any live demos
Timing note	Session 1 ≈ 75 min of review (segments 1–7). Session 2 ≈ 75 min: exam administration + send-off.

SESSION 1 — The Cumulative Review (~75 min)

Segment 1 — Opening Map: the Whole Course on One Board (10 min)

Hook. "Eighteen weeks ago, a statistic was a number someone told you. Today you can interrogate one from every side. Let's draw everything you own."

Draw the course as four rooms in one house (the deck's map slides mirror this — students will photograph them):

Describing data (W1–4): who was measured and how (population/sample, sampling, bias) → pictures (histograms, shape) → numbers (mean/median, SD/IQR, z-scores) → pairs (scatterplots, r, two-way tables).
Chance & models (W5–8): probability rules → random variables and E(X) → the binomial → the normal model and the z-table.
From samples to estimates (W10–12): sampling distributions and the CLT (σ vs. σ/√n) → t-intervals for means → z-intervals for proportions, sample size.
Tests, tables & lines (W13–17): the courtroom logic (H₀/Hₐ, p-value, α, error types) → t-tests for means and paired data → z-tests for proportions, two samples → chi-square for count tables → regression with slope inference.

Say it plainly: "The final walks these four rooms in order — about 24 questions from the first half, about 36 from the second, because the inference half is where the course was headed all along."

Segment 2 — Rapid-Fire Round 1: Describe & Model (W1–8) (15 min)

Fire these fast — students answer solo on paper (30 seconds each), then call the answers. Every answer is stated below; all arithmetic is pre-verified.

#	Prompt	Answer
R1	Classify: a player's jersey number.	Nominal — a number that labels; averaging it is nonsense.
R2	14 of the 56 audited receipts show an error. Relative frequency?	14 ÷ 56 = 0.25.
R3	Incomes are right-skewed. Which center do you report, and why?	The median — it resists the tail's pull.
R4	Mean 25, SD 4. What's the z-score of 33?	(33 − 25) ⁄ 4 = z = 2.0.
R5	P(A) = 0.3. P(not A)?	1 − 0.3 = 0.7.
R6	X takes value 1 or 2, each with probability 0.5. E(X)?	1(0.5) + 2(0.5) = 1.5.
R7	Binomial, n = 25, p = 0.2: mean and SD of the count?	Mean 25 × 0.2 = 5; SD √(25 × 0.2 × 0.8) = √4 = 2.
R8	Course z-table: area to the left of z = 1?	0.8413.
R9	σ = 10, n = 25. Standard error of the sample mean?	10 ⁄ √25 = 2 — the ruler for averages, not individuals.
R10	df for a one-sample t with n = 16? And for a regression slope?	15 (n − 1) — and a slope uses n − 2.

Debrief the two that wobble: R1 (numbers that label) and R9 (SD vs. SE — "two rulers" — say it twice).

Segment 3 — Worked Integration Example 1: From Raw Data to an Honest Interval (10 min)

Do every step on the board. This chains W3 → W10 → W11 in one arc.

A grower pulls a random sample of 16 greenhouse temperature readings: x̄ = 21.0 °C, s = 2.0 °C. Build the 95% confidence interval for the mean reading.
1. Conditions: random sample; n = 16 is small, so we need no strong skew/outliers — the histogram looks fine (say you checked).
2. SE = s ⁄ √n = 2.0 ⁄ 4 = 0.5 °C — the wobble of the mean, not of one reading.
3. t*: df = 15, 95% → 2.131 (the Week 11 table, printed in the study guide).
4. ME = 2.131 × 0.5 = 1.0655 → interval = 21.0 ± 1.0655 → (19.93, 22.07) °C (round at the end).
5. Say it: "We are 95% confident the interval 19.93 to 22.07 °C captures the mean reading — a statement about the method's capture rate, never about 95% of individual readings."

The trap to name: swapping s for SE (using 2.0 instead of 0.5 quadruples the margin) and reading the interval as covering individuals.

Segment 4 — Rapid-Fire Round 2: Infer & Decide (W10–17) (15 min)

#	Prompt	Answer
R11	t* for a 99% interval, n = 10?	df 9 → 3.250 — little data + big promises = the widest cushion.
R12	What exactly is "95% confident" about?	The method: about 19 of every 20 random samples produce a capturing interval.
R13	p-value 0.03, α = 0.05. Decision?	Reject H₀ — and say it in context, never "accept."
R14	Group 1: 12 successes of 60. Group 2: 18 of 40. Pooled proportion?	(12 + 18) ⁄ (60 + 40) = 30 ⁄ 100 = 0.30.
R15	Goodness-of-fit with 4 categories: df?	4 − 1 = 3.
R16	A plan claims 25% of 120 orders. Expected count?	120 × 0.25 = 30.
R17	"Fail to reject H₀" means…?	The data don't give convincing evidence against H₀ — not that H₀ is proven.
R18	Which test: same 12 people measured twice?	Paired t — one-sample t on the differences.

Segment 5 — Worked Integration Example 2: A Claim on Trial, Start to Finish (10 min)

This chains W12 → W13 → W15, and ends on the decision-map skill the final rewards.

A pub-quiz platform claims half of all teams return the following week. A skeptic samples 100 random teams: 40 returned.
1. Name the shape of the answer: one sample, a yes/no outcome, a claimed percentage → one-proportion z-test. (Mean? No — nothing is being averaged.)
2. Hypotheses: H₀: p = 0.50 vs. Hₐ: p ≠ 0.50 (no direction was called in advance).
3. Conditions: np₀ = 50 ≥ 10, n(1 − p₀) = 50 ≥ 10, random sample. ✓
4. SE under H₀ = √(0.5 × 0.5 ⁄ 100) = 0.05; z = (0.40 − 0.50) ⁄ 0.05 = −2.0.
5. p-value (course z-table): 2 × (1 − 0.9772) = 0.0456 ≤ 0.05 → reject H₀: convincing evidence the true return rate isn't one-half.
6. Close the loop: "Significant — and is a 40%-vs-50% gap practically important? For a business, probably yes. Always ask both questions."

Segment 6 — Misconception Clinic: the Greatest Hits (10 min)

Put each wrong sentence on the board; have the room repair it aloud before you confirm:

❌ "Bigger samples fix bias." → ✅ Bias is baked into the method (Week 1's 2.4-million-ballot lesson: method beats size).
❌ "If it's a number, it's quantitative." → ✅ Route numbers, IDs, zip codes label — NOIR before arithmetic.
❌ "Correlation proves causation." → ✅ A handshake, not a push; hunt the lurking variable; only random assignment earns a causal verb.
❌ "The SD of the data is the SE of the mean." → ✅ Two rulers: σ for individuals, σ⁄√n for averages.
❌ "95% confident = 95% of individuals are inside." → ✅ Confidence describes the method's capture rate for the parameter.
❌ "p-value = the probability H₀ is true." → ✅ It's P(data at least this extreme assuming H₀).
❌ "Fail to reject = accept." → ✅ Absence of convincing evidence is not proof of absence.
❌ "Significant = important." → ✅ Huge samples flag tiny effects; ask "how big?" right after "how surprising?"
❌ "A line predicts anywhere." → ✅ Outside the fitted range, the line is fiction — refuse to extrapolate.

Segment 7 — Exam Logistics + Q&A (5 min)

Format: 60 auto-graded questions (mostly multiple choice, a few true/false, select-all, and matching), 2 points each, 120 total, one attempt, answer order shuffled.
Coverage: cumulative — roughly 24 questions from Weeks 1–8 and 36 from Weeks 10–17. Every computation lands on the course's three embedded tables (z, t, chi-square) or on clean arithmetic.
Allowed: a calculator, and one page of notes if your instructor permits it (announce your policy now). The needed z, t, and chi-square values are stated inside any question that requires them.
Not allowed: AI tools of any kind, collaboration, or course materials beyond the permitted note page.
Weight: 5% — say it out loud one more time: a checkpoint, not a verdict. Then take questions.

SESSION 2 — The Final Exam + Course Send-off (~75 min)

Administration notes (instructor-facing):

Recommended window: open the exam at the start of the session; 60 minutes is a comfortable budget for 60 items (≈1 minute each); reserve the final ~10 minutes for the send-off. Async sections: a 75-minute timer inside a one-day window mid-week mirrors this.
Remind students before they begin: closed to AI; one attempt; flag-and-return works because all 60 items are visible; every lookup value needed is printed in the question.
Accessibility: honor extended-time accommodations; the QTI import carries no time limit, so set timing in your platform.
If a student finishes very early, quietly invite a second pass on flagged items — the most common lost points are misread "at least/at most" and SD-vs-SE swaps.

Course send-off (last ~10 minutes, after papers/submissions are in):

Name what they built, out loud, in one arc: ask who was measured → picture the data → summarize it → model the chance → estimate with honesty → test with discipline → and choose the right tool without being told which.
Callback to the very first session: the three questions (Who was measured? How were they picked? What was actually recorded?) — "you will never read a poll, a rating, or a 'studies show' the same way again."
Practical close: grades post per the syllabus timeline; the chapters and study guide remain theirs to keep; statistics shows up in every field they're headed to — invite them to keep the decision map.
Last line, verbatim if you like: "Eighteen weeks ago a statistic was a number someone told you. Now it's a claim you can question. That's the whole course — go use it."

Instructor FAQ — Final-Week Stumbles

Student says / does	Quick cure
"Is the final worth cramming for?"	It's 5% — a checkpoint. The efficient path is the bundle in order: study guide → practice exam → exam-prep tutorial. Two focused hours beat one long night.
"Will there be questions about the penguin dataset?"	No exam question depends on remembering any dataset. Concepts and fresh scenarios only.
"Do I need to memorize the z, t, or chi-square tables?"	No — any question needing a lookup value states it. Students should know how to use a stated value, not recall it.
"Can I use my chatbot on the practice exam?"	Yes — practice is open and ungraded (that's the point). The final itself is closed to AI, like every quiz all term.
"The practice exam felt different from the real one."	By design: it practices the same skills with zero shared questions, so it measures readiness, not memory.
"I blanked on which test to use."	Re-run the decision map: is the answer a mean, a proportion, counts in categories, or a line? One sample, two samples, or the same individuals twice? The shape of the answer names the tool.
Confuses s with SE on interval problems.	The final's most common lost point all term. Chant it: s describes individuals; s⁄√n describes the mean.
"What happens if I fail it?"	Arithmetic first: at 5%, the difference between a strong and a weak final is about 2–3 points of the course grade. The weekly work has already decided most of the story.

Scope flag

This outline introduces no new content. Every drill, example, and table value comes from Weeks 1–17 as taught (z-table from Week 8; t-table from Week 11; chi-square critical values from Week 16). The two integration examples use fresh numbers that appear on no graded assessment. If your section runs short, cut Segment 6 to the four misconceptions your gradebook says your students actually hold.