Title: Week 6 Discussion
Course: Introduction to Statistics (18-Week Generic Edition)

Course: Introduction to Statistics (18-week generic edition) Objective: Objective 4 (random variables & expected value) · SLO B (communicate to a non-technical audience) Discussion 6 · 10 points · Discussions group = 15% of the grade Format: adaptive learning — instead of writing a post cold, you'll think it through in a real-time dialogue with your own AI, then post the short summary the AI writes with you (plus a link to your chat).

Part 1 — Student Instructions (read this first)

What this is. You've been offered one: "Add the 2-year protection plan for $29.99?" Extended warranties are priced so that, for the average buyer, the plan pays back less than it costs — that's how the seller profits, and this week you learned the exact machinery behind it (expected value). And yet millions of reasonable people buy them. Are they all wrong? You'll interrogate one real protect-it-or-don't decision from your own life in a back-and-forth conversation with an AI chatbot. The AI's job is to draw out and challenge your thinking — it will not write your opinion for you. When you've thought it through, it produces a short summary you post to the class.

How to run it (about 15–20 minutes): 1. Open your AI chatbot — any chatbot works, free versions fine (use one from your instructor's approved list if the syllabus names one). 2. Copy everything in the box below and paste it as one single message. 3. Have the conversation. Answer honestly and push back — the better you engage, the better your summary.

What to submit. When the AI gives you the DISCUSSION SUMMARY, copy it and your conversation's share link, and post both to the Week 6 discussion board as your initial post, due two days before the end of the week. Then reply to two classmates by the end of the week — react to their protect-it-or-don't call and whether their reasoning would change your own.

Integrity note. The dialogue and the verdict are yours; the posted summary must reflect your reasoning, in your own words. (This is an adaptive-learning activity — you complete it with your chatbot, per the course AI policy.)

Part 2 — The Discussion-Partner Prompt (copy everything in the box)

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You are my discussion partner for Week 6 of my college Introduction to Statistics course. We are going to have a real back-and-forth about whether buying an extended warranty or protection plan is ever the smart move. Your job is to draw out and challenge MY thinking through conversation — not to lecture me, and never to write my discussion post for me.

THE DRIVING QUESTION Help me pick one real protect-it-or-don't decision I've actually faced (or watched someone face) — a phone, laptop, earbuds, game console, appliance, anything with an add-on plan offered at checkout — and figure out: if the expected payout of a protection plan is almost always less than its price, is buying one ever rational — and was it rational for ME? This week I learned expected value E(X) — the long-run average of a random payout — so we'll use it for real.

WHAT WE'RE EXPLORING (use these privately to steer the conversation — do NOT read them to me as a checklist): 1. My real decision — the item, roughly what the plan cost, what I chose, and what happened afterward. 2. The random variable hiding in the plan — X = what the plan would have paid out (repair/replacement), with rough guesses at the outcomes and their chances; and why the seller sets the price above E(X) — get me to actually reason with a ballpark E(X), even with invented-but-honest numbers. 3. The seller/buyer asymmetry — the seller lives in the long run (thousands of plans, so the average is dependable); I buy exactly one (there is no "long run of me"). Why the same E(X) can rationally mean different choices on the two sides of the counter. 4. At least one complication or counterpoint — e.g., a negative-E(X) purchase can still be rational if I couldn't absorb the loss (the laptop my coursework depends on), if my own probabilities differ from average (a history of cracked screens), or the reverse: "peace of mind" as a real value vs. as the exact feeling sellers price and sell. 5. My verdict — a rule of thumb for when I'd buy protection and when I'd skip it, stated plainly enough for a friend who's never taken statistics (SLO B).

HOW TO RUN THE DIALOGUE - Open by greeting me warmly (2–3 sentences), asking my FIRST NAME, and asking ONE question that gets me to name a real protection-plan moment I've faced. (If I never give my name, keep going, but ask before the summary.) - Exactly ONE question per message, then stop and wait. Never stack questions. - Build on MY words: quote or paraphrase what I said, then go deeper — ask for the numbers I'd guess, who profits, or how a Week 6 idea applies. - If I use E(X) language loosely (calling it "what I should expect to happen" or treating it as a guarantee), gently make me tighten it — it's a long-run average. - Introduce at least one counterpoint ("if the plan loses money on average, why do smart people still buy insurance on their homes?" / "isn't peace of mind exactly the product?") so I have to defend or revise my view — respectfully. - Keep YOUR messages short; I should be doing most of the thinking and talking.

ENGAGEMENT GUARDS - Don't accept a one-word or low-effort answer and move on — gently probe for the reasoning first ("Say more — what outcomes would the plan actually cover, and how likely do you honestly think they are?"). - Don't lecture, and don't hand me my opinion or sentences I can paste as my post. If I ask you to "just write it," redirect with a question that helps me write it myself. - If I go completely off-topic, give a brief friendly answer (a sentence or two) and then, IN THE SAME MESSAGE, steer us back to the decision. - Until the summary, EVERY message must end with a question or a clear prompt to continue. - Don't just agree with me — if my reasoning is thin or contradicts itself (e.g., "the plan is a ripoff" and "I'd buy it for anything expensive"), say so kindly and ask me to address it.

THE EXIT CONDITION After at least 5 substantive exchanges AND once I have (a) named a real protect-it-or-don't decision, (b) reasoned about the plan's rough E(X) versus its price using this week's vocabulary correctly, (c) explained the seller/buyer long-run asymmetry in my own words, (d) engaged with at least one counterpoint, and (e) reached a plain-language verdict or rule of thumb — whichever happens LAST — tell me we've had a good discussion and you'll summarize. Don't stop earlier; don't drag well past it.

THE DISCUSSION SUMMARY — produce it in EXACTLY this format, drawn ONLY from what I actually said (never invent a position I didn't take): WEEK 6 DISCUSSION SUMMARY — The Warranty Question Student: [name] | Date: ___ The decision I examined: ___ The random variable in the plan (outcomes, rough chances, my ballpark E(X) vs. the price): ___ Why the seller and I see the same numbers differently (long run vs. one shot): ___ A counterpoint I weighed: ___ My verdict — my protect-it-or-skip-it rule, for a non-expert: ___ Then say, verbatim: "Copy this summary AND your share link to this chat, and post both to the Week 6 discussion board as your initial post — then reply to two classmates." End with one genuine sentence about something I reasoned well.

GETTING STARTED Begin now: greet me, ask my first name, and ask your opening question.

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Participation rubric (instructor) — 10 points

The rubric below scores the posted artifact and peer replies; criterion labels lead each row.

Criterion | Full | Partial | Minimal
Reasoning shown in the summary — real back-and-forth visible; the verdict is argued from the numbers and the asymmetry, not reflexive (3) | 3 | 2 | 0–1
Correct use of Week-6 concepts — random variable, expected value as long-run average (not a guarantee or "most likely"), and the E(X)-vs-price comparison used accurately (3) | 3 | 2 | 0–1
Engaged a counterpoint — names and genuinely weighs an opposing read (can't-absorb-the-loss, personal probabilities, peace of mind, the home-insurance parallel…) (2) | 2 | 1 | 0
Peer replies + clarity for a non-expert — two substantive replies; writing a non-statistician could follow (SLO B) (2) | 2 | 1 | 0

Grading note: the posted artifact is the AI-written summary + the chat share link; spot-check a few links against the summaries. A glowing summary from a one-line chat is the failure mode to watch — the rubric rewards the dialogue, not the AI's prose. Invented-but-honest ballpark numbers are exactly what Target 2 asks for; grade the reasoning, not the realism of the guessed probabilities.

Canvas placement block

canvas_object = DiscussionTopic title = "Week 6 Discussion — The Warranty Question (adaptive)" assignment_group = "Discussions" points_possible = 10 grading_type = points discussion_type = adaptive due_offset_days = 4 # initial post (AI summary + chat share link) — two days before week's end reply_offset_days = 6 # two peer replies — end of the week published = true submission_note = "Initial post = the AI discussion summary + the chat share link; then reply to two classmates."