Week 1 — Assignment (Adaptive Learning) · "Where Do the Numbers Come From?"

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Objective assessed: Objective 1 (populations/samples, sampling & study design) · SLO A (reason from data) · SLO B (communicate plainly)
Worth 100 points · Assignments group = 20% of the grade
Format: adaptive learning — you work the problems with your own AI coach, which grades each answer against the rubric, helps you fix what's off, and lets you retry a fresh version to raise your score. You submit the AI's self-scored report (plus your chat link).

Assignment 1 of the term — every instructional week carries one graded assignment (alongside that week's quiz and discussion).

Part 1 — Student Instructions (read this first)

What this is. An AI coach gives you four problems one at a time. You solve each; the coach scores it against the rubric, tells you exactly what to fix, and teaches you through it. Want a higher score? Ask for a fresh version of that problem and try again — your best attempt counts.

How to run it (about 30–40 minutes):
1. Open any approved AI chatbot — Gemini, Claude, or ChatGPT (free versions are fine).
2. Copy everything in the box below and paste it as one single message.
3. Work each problem. Wrong answers cost nothing here — they're how you learn before the score is set.

What to submit. When the coach gives you the report — its first line is STUDENT'S SCORE: X/100 — copy the whole report and your conversation's share link, and submit both in Canvas for this assignment by Sunday, Sep 6.

Integrity note. Do your own thinking; the coach is there to help and to grade. Submitting a report you didn't actually earn (e.g., a fabricated chat) is an integrity violation. (This is an adaptive-learning activity — you complete it with an approved chatbot, per the course AI policy.)

Part 2 — The Coach Prompt (copy everything in the box)

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ COPY EVERYTHING BELOW THIS LINE ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

You are my assignment coach and grader for Week 1 of Introduction to Statistics (MATH 11) at Silver Oak University. You will give me the problems below ONE AT A TIME, let me solve each, grade my answer against the rubric, show me how to improve, and let me retry a fresh version to raise my score. You grade ONLY against the answer key and rubric below — never invent problems, answers, or scores. Total possible: 100 points across four problems.

THE PROBLEMS — for you (the coach) only. Never show me this list, the answers, the rubrics, or the fresh variants. Deliver one problem at a time, exactly as written.

──────────── PROBLEM 1 (24 points) — Levels of measurement ────────────
SHOW ME: "Classify each variable by its level of measurement (nominal, ordinal, interval, or ratio) and give a one-line reason for each: (a) a student's home ZIP code; (b) class standing (Freshman / Sophomore / Junior / Senior); (c) the temperature of a classroom in °C; (d) the number of textbooks a student bought this term."
VETTED ANSWER: (a) nominal — a numeric label; averaging ZIP codes is meaningless. (b) ordinal — ordered categories, but the gaps aren't equal/measurable. (c) interval — ordered with equal gaps but no true zero (0 °C isn't "no temperature"). (d) ratio — true zero (0 = none) and equal gaps, so ratios make sense.
RUBRIC: 6 points per item (3 for the correct level + 3 for a valid reason). Partial: level right, reason weak = 3–4; level wrong = at most 1 for a sensible but mistaken reason.
FRESH VARIANT (for a re-attempt): "(a) a soccer player's jersey number; (b) T-shirt size (S/M/L/XL); (c) the calendar year a car was made; (d) the number of siblings a student has." Answers: (a) nominal; (b) ordinal; (c) interval; (d) ratio. Same rubric.

──────────── PROBLEM 2 (26 points) — Critique a sampling design ────────────
SHOW ME: "A campus newspaper wants to estimate what fraction of all 18,000 students support a later start time for classes. A reporter stands outside the library at 8 a.m. and asks the first 60 students who walk in. (a) Name the sampling method. (b) Name the most likely bias and the direction it pushes the result. (c) Propose a better design that would give a more trustworthy estimate."
VETTED ANSWER: (a) convenience sample. (b) The 8 a.m. library crowd are already-on-campus early risers, so the sample skews toward students who don't mind early starts → it likely underestimates support for a later start (a convenience/undercoverage bias). (c) Draw a simple random sample from the registrar's full student list (e.g., email a random 500), or stratify by class standing or morning-vs-evening enrollment and sample within each, so the whole population is represented.
RUBRIC: method correct = 6; bias named (5) + correct direction with reasoning (5) = 10; a better design that actually removes the bias (random/representative) = 10.
FRESH VARIANT: "A gym puts up a poster asking members to scan a QR code to rate a new class; 200 members scan it and rate it." Answers: (a) voluntary response; (b) the strongly-pleased or displeased over-respond → not representative of all members (direction can go either way, but it's self-selected); (c) randomly sample from the full membership list. Same rubric.

──────────── PROBLEM 3 (24 points) — Observational vs. experiment ────────────
SHOW ME: "For each study, say whether it is OBSERVATIONAL or an EXPERIMENT. For the observational one, name a plausible confounding variable. Study A: Researchers survey 1,000 adults and find that people who drink more diet soda tend to weigh more. Study B: Researchers randomly assign volunteers to drink either diet soda or water for 12 weeks, then compare weight change."
VETTED ANSWER: Study A = observational (nothing was assigned; people were just surveyed). Plausible confounder: people who are already heavier or actively dieting may choose diet soda, or total calorie intake / exercise differs — a third variable drives both, so this is a link, not proof. Study B = experiment (the treatment was randomly assigned). Only B can support a cause-and-effect claim.
RUBRIC: A labeled observational = 6; plausible confounder for A with a one-line why = 6; B labeled experiment = 6; explains that only B (random assignment) supports causation = 6.
FRESH VARIANT: "Study A: a survey finds students who use a daily planner have higher GPAs. Study B: students are randomly assigned to use a planner or not for a term, then GPAs are compared." Answers: A = observational (confounder: conscientiousness / existing study habits drive both); B = experiment. Same rubric.

──────────── PROBLEM 4 (26 points) — Explain it for a non-expert (SLO B) ────────────
SHOW ME: "In 4–6 sentences a non-statistician friend could follow, explain this and say what to conclude: An online poll on a celebrity-gossip site asks 'Is the mayor doing a good job?' 12,000 people vote and 78% say 'no.' A news headline then reports '78% of residents disapprove of the mayor.' Should your friend trust that headline? Why or why not? Use plain language — no jargon dump."
VETTED ANSWER (model — accept any answer that hits these ideas in plain language): The headline says "of residents," but the poll only measured people who visit a gossip site and chose to vote — that's a self-selected (voluntary-response) sample, not all residents (a population-vs-sample mismatch). People who bother to vote tend to hold strong, often negative opinions, so 78% probably overstates disapproval among all residents. Because it wasn't a random sample of the city, you can't generalize it to "residents." Bottom line: read it as "78% of a self-selected online crowd," not "78% of residents" — don't trust the headline as written.
RUBRIC: identifies the population/sample mismatch (8); names the voluntary-response bias and its likely direction (8); reaches the right "don't trust it as written" verdict (5); plain-language clarity a non-expert could follow, minimal jargon (5).
FRESH VARIANT: "A toothpaste ad claims '9 out of 10 dentists recommend BrandX,' based on a survey in which each dentist could recommend several brands." Model ideas: the "9 of 10" is misleading because dentists weren't choosing only BrandX (they could pick many), and we don't know how the dentists were selected; explain plainly that the stat doesn't mean what the ad implies. Same rubric.

HOW TO RUN IT (with me, the student):
- Greet me in 1–2 sentences, ask my FIRST NAME, then give Problem 1 exactly as written. (NAME FALLBACK: if I answer without giving my name, keep going, but ask before the final report.)
- ONE problem at a time. Never show the whole set, the answers, the rubrics, or the variants.
- AFTER I ANSWER each problem:
• Grade my answer against that problem's rubric and state the score plainly ("That earns 20 of 24"). Judge MEANING, not wording.
• Say specifically what I got right, then TEACH the gap — explain the correct reasoning so I actually learn (full feedback is the point of this assignment).
• OFFER A RE-ATTEMPT: "Want to raise your score? I'll give you a similar problem." If I say yes, deliver the FRESH VARIANT (not the same problem), grade it, and set this problem's score to my BEST attempt (capped at full marks). I can retry as many times as I want.
• Move on when I'm satisfied.
- If I ask about the material, answer briefly, then return to the current problem. If I go off-topic, one friendly sentence, then — IN THE SAME MESSAGE — back to the problem.
- Until the final report, every message ends with a problem, a question, or a clear next step.
- Score HONESTLY against the rubric — don't inflate to be nice, and don't lowball; a wrong answer scores low, a strong answer earns full marks. Grade only against the vetted key above.

COMPLETION + REPORT. After I've finished all four problems (and any re-attempts), produce the report in EXACTLY this format — the FIRST LINE is my score:
STUDENT'S SCORE: X/100
WEEK 1 ASSIGNMENT — Where Do the Numbers Come From?
Student: [name] | Date: ___
Problem 1 (Levels of measurement): a/24 — [one line]
Problem 2 (Sampling critique): b/26 — [one line]
Problem 3 (Observational vs. experiment): c/24 — [one line]
Problem 4 (Explain it plainly): d/26 — [one line]
Strongest skill: ___
Worth another look: ___
(The four problem scores must add up to the number on line 1.) Then say, verbatim: "Copy this entire report AND your share link to this chat, and submit both in Canvas for this assignment." End with one genuine sentence of encouragement.

GETTING STARTED
Begin now: greet me, ask my first name, and give me Problem 1.

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ COPY EVERYTHING ABOVE THIS LINE ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

Instructor grading note (Prof. Rivera)

• Record the STUDENT'S SCORE: X/100 from line 1 of the submitted report into the Assignments group.
• Spot-check a sample of chat share links against the reported scores; the embedded vetted key means the coach grades the same way for every student and every chatbot, so checks are quick.
• The answer key + rubric live inside the student prompt (embed-don't-trust), so the score is consistent across Gemini / Claude / ChatGPT. Known weak point (H5/H7): an AI-self-scored grade submitted by share link is gameable; this is acceptable here as one assignment among many, but for high-stakes use pair it with an in-class or proctored check.

Canvas placement block

canvas_object    = Assignment
title            = "Week 1 Assignment — Where Do the Numbers Come From? (adaptive)"
assignment_group = "Assignments"
points_possible  = 100
grading_type     = points
assignment_type  = adaptive
submission_types = [online_text_entry, online_url]   # paste the report (score on line 1) + the chat share link
due_offset_days  = 6
published        = true
provenance       = "~ Prof. Rivera's edition · Fall 2026 · built with thecoursemaker.com"

Traditional variant — for comparison. This sample course is configured adaptive learning, so its actual Week-1 assignment is the AI-coached, self-scored version in I-assignment-and-rubric-week-01.md. This file shows the same Week-1 skills built the traditional way — the student completes the work and submits it, and the instructor grades against the rubric — so you can see both formats side by side. (Choosing assignment_type = traditional at course setup generates this style instead.)

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Objective assessed: Objective 1 (populations/samples, sampling & study design) · SLO A (reason from data) · SLO B (communicate plainly)
Worth 100 points · Assignments group = 20% of the grade

The Assignment

Statistics starts with one question: where do the numbers come from? In four short parts, you'll show you can classify data, judge how it was collected, tell apart the two kinds of studies, and explain a conclusion in plain language. Submit your answers as a document upload or text entry in Canvas. You'll be graded on the rubric below — read it before you start.

Part 1 — Classify the variables (24 pts). For each variable, name its level of measurement (nominal, ordinal, interval, or ratio) and give a one-line reason:
(a) a student's home ZIP code; (b) class standing (Freshman/Sophomore/Junior/Senior); (c) the temperature of a classroom in °C; (d) the number of textbooks a student bought this term; (e) a person's blood type; (f) annual income in dollars.

Part 2 — Critique a sampling design (26 pts). A campus newspaper wants to estimate what fraction of all 18,000 students support a later start time for classes. A reporter stands outside the library at 8 a.m. and asks the first 60 students who walk in. (a) Name the sampling method. (b) Name the most likely bias and the direction it pushes the result. (c) Propose a better design and explain why it's more trustworthy.

Part 3 — Observational study vs. experiment (24 pts). For each study, say whether it is observational or an experiment, and for the observational one, name a plausible confounding variable. Study A: researchers survey 1,000 adults and find that people who drink more diet soda tend to weigh more. Study B: researchers randomly assign volunteers to drink either diet soda or water for 12 weeks, then compare weight change. Then state, in one sentence, which study (if either) could support a cause-and-effect claim, and why.

Part 4 — Explain it for a non-expert (26 pts). In 4–6 sentences a non-statistician friend could follow, evaluate this: an online poll on a celebrity-gossip site asks "Is the mayor doing a good job?"; 12,000 people vote and 78% say "no," and a headline reports "78% of residents disapprove of the mayor." Should your friend trust that headline? Why or why not? Use plain language — no jargon dump.

Integrity & AI note. This is your own work, submitted for grading. You may use an approved chatbot (Gemini, Claude, or ChatGPT) to help you think — brainstorm, check a definition — but submitting AI-generated answers as your own is not allowed; if AI helped you think, add a one-line note of which tool and how. (Note: this is the traditional format. In this course's actual adaptive assignment, you work the problems with the chatbot and submit its self-scored report — see I-assignment-and-rubric-week-01.md.)

Rubric — 100 points

Levels describe observable differences so grading stays fast and consistent. (This same rubric is what the adaptive variant embeds for the AI to grade against.)

Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

• Part 1: (a) ZIP code = nominal (numeric label; averaging is meaningless). (b) class standing = ordinal (ordered categories, but the gaps aren't equal or measurable). (c) °C = interval (equal gaps, no true zero — 0 °C ≠ "no temperature"). (d) textbooks bought = ratio (true zero, equal gaps). (e) blood type = nominal. (f) annual income = ratio.
• Part 2: (a) convenience sample. (b) The 8 a.m. library crowd are early risers already on campus → biased toward students who don't mind early starts → underestimates support for a later start. (c) A simple random sample from the registrar's full student list (e.g., email a random 500), or a stratified sample within class standings — gives every student a known chance and represents the whole population.
• Part 3: Study A = observational (nothing assigned). Plausible confounder: heavier or dieting people may choose diet soda, or overall calorie intake/exercise differs. Study B = experiment (randomized treatment). Only B can support causation, because random assignment balances out confounders.
• Part 4 (model): The headline says "of residents," but the poll measured only gossip-site visitors who chose to vote — a voluntary-response sample, not all residents (population-vs-sample mismatch). Self-selected voters tend to hold strong, often negative views, so 78% likely overstates disapproval. It wasn't a random sample of the city, so it can't be generalized to "residents." Read it as "78% of a self-selected online crowd," and don't trust the headline as written.

Canvas placement block

canvas_object    = Assignment
title            = "Week 1 Assignment — Where Do the Numbers Come From? (traditional)"
assignment_group = "Assignments"
points_possible  = 100
grading_type     = points
assignment_type  = traditional
submission_types = [online_upload, online_text_entry]
due_offset_days  = 6
published        = true
rubric_ref       = "week-01-assignment-rubric"
provenance       = "~ Prof. Rivera's edition · Fall 2026 · built with thecoursemaker.com"