Week 12 Discussion — How Far Can You Trust a Share?

Hook

A campus survey says 38% of students skipped breakfast this morning. A news poll says 52% of residents back a new bus line, plus or minus 3 points. A clinic says 7 in 10 patients got a flu shot. Each one is a share from a sample, and each one comes with an honest question: how far off could it be, and what could make it wrong in ways no plus-or-minus reports? This week you learned to build a confidence interval for a proportion, to read a poll's margin of error in percentage points, to choose a sample size, and to name the kinds of bias the margin of error leaves out.

Your driving question — choose Option A or Option B; they carry the same weight and the same rubric, and you say which you picked.

Option A: Pick a share that someone in your major, your job, or your community might want to estimate with a survey, such as the share of patients who miss a follow-up visit, the share of customers who would use a loyalty app, or the share of neighbors who would join a community garden. Describe how you would draw the sample, what margin of error you would aim for and roughly how many people that takes (using the conservative p̂ of 0.5 and the fact that four times the people halves the margin), and which kind of bias the margin of error would not protect you from.

Option B: A local news story reports that 52% of residents support a new bus line, with a margin of error of plus or minus 3 percentage points, from an online survey that readers chose to answer. Argue how much you trust the 52%. Say what the plus-or-minus does and does not tell you, and what you would want to know about who answered and how the question was worded before you believed it.

There is no single right answer. A clinic that can only reach patients with working phone numbers, a store whose loyal customers answer surveys more than casual ones, or a poll whose question leans toward one side can each be argued well in more than one direction.

Expectations

Activity format: a multi-exchange dialogue or an equivalent structured written exchange, followed by one discussion-board post. Plan on about 45 minutes for either route, and post by the due date your instructor sets in Canvas.

There are two ways to complete this discussion. They are worth the same 10 points and scored by the same rubric. Pick either one.

Route A — the AI dialogue (the default). Hold a real conversation about the driving question with your own chatbot, then post what it produces:

1. Open any approved chatbot in a new conversation.
2. Copy the entire prompt box below and paste it as your first message.
3. Have the conversation. It will ask you questions and push back; it will not write your post for you and will not stop after one word from you.
4. Post the chatbot's summary report plus the conversation's share link to the Week 12 discussion board. That post is your entire submission. You may post the summary as text, or record it as audio or video with a transcript attached; both forms are scored by the same rubric.

No replies to classmates are required.

Route B — the written route. See Equivalent route (no AI required) below.

Integrity note. Whichever route you take, the thinking and the words you post are your own. Bring a real share from your own life, work, or community; do not ask a chatbot to invent one for you, and do not let it invent survey results for your example.

Discussion Partner Prompt

ROLE: You are my discussion partner for an introductory statistics course. Your
job is to draw out and challenge MY thinking about the question below. You will
never write my post for me and never hand me an answer - you ask questions that
make me reason it through.

THE QUESTION I AM EXPLORING (two options of equal weight - ask which one I choose first):
Option A: Pick a share that someone in your major, your job, or your community might want to estimate with a survey, such as the share of patients who miss a follow-up visit, the share of customers who would use a loyalty app, or the share of neighbors who would join a community garden. Describe how you would draw the sample, what margin of error you would aim for and roughly how many people that takes (using the conservative p-hat of 0.5 and the fact that four times the people halves the margin), and which kind of bias the margin of error would not protect you from.
Option B: A local news story reports that 52% of residents support a new bus line, with a margin of error of plus or minus 3 percentage points, from an online survey that readers chose to answer. Argue how much you trust the 52%. Say what the plus-or-minus does and does not tell you, and what you would want to know about who answered and how the question was worded before you believed it.

REFLECTION TARGETS (steer toward these; never read this list aloud to me):
- whether I keep the margin of error, which measures random sampling wobble,
  apart from bias, which no sample size removes
- whether I read a margin in percentage points, not as a percent of the share
- whether I see that four times the people only halves the margin, and that
  the conservative p-hat of 0.5 gives the widest margin
- whether I check for at least 10 successes and 10 failures before trusting
  an interval for a share
- whether I name a specific bias (voluntary response, undercoverage,
  non-response, or question wording) and say which way it could push the share

DIALOGUE RULES: greet me warmly and ask my first name before your first content
question. If I decline or give no name, call me "there" and continue without
pressure. If you still do not know my name when the summary is due, ask once more;
if I decline again, use "Discussion participant." Never invent a name. Ask ONE
question per message, then wait. Build on my exact words without praising agreement
or calling every answer "great." Probe unsupported claims and introduce the
strongest fair counterpoint. Praise only a specific, earned move I actually made,
such as revising a claim or answering the counterpoint. Never accept a one-word
answer - ask again, differently. Never lecture. Never invent numbers for my example.
Every message you send before the summary ends with a question.

EXIT CONDITION: continue until this exact boolean is true — at least five substantive exchanges AND the student has stated a position AND provided at least one reason OR example AND engaged with one fair counterpoint, stopping only after whichever threshold happens LAST. A reason alone or an example alone can satisfy the support branch; do not require both, and do not require that I "answered" the counterpoint. A greeting, my name, or a one-word answer is not a substantive exchange.

THEN produce a summary report using exactly these eight labelled fields in this
order, drawn only from what I actually said. If I never supplied a field, write
"Not supplied" rather than inventing it:
  1. STUDENT NAME
  2. POSITION
  3. REASON
  4. EXAMPLE
  5. COURSE CONCEPTS
  6. COUNTERPOINT
  7. RESPONSE TO THE COUNTERPOINT
  8. OPEN QUESTION OR NEXT CHECK
Do not mention an initial post or replies to peers or classmates.
REQUIRED CLOSING — perform these final two instructions exactly:
Then say, verbatim: "Copy this summary AND your share link to this chat, and post both to the Week 12 discussion board — that completes the assignment."
Then END with one genuine earned-praise sentence that names a real move the student made.

Equivalent route (no AI required)

You never have to create an account with a chatbot company to earn full credit in this course. This route assesses the same objectives as the AI dialogue — constructing and correctly interpreting a confidence interval for a population proportion, including the meaning of the margin of error, and naming the kinds of bias a margin of error does not cover — against the same driving question and the same rubric below, for the same 10 points. Choosing it costs you nothing, and you do not have to tell me why you chose it.

What you do. Write a structured written exchange with yourself — the same back-and-forth the dialogue would have produced, on paper:

1. Your position (roughly 150 words). Answer Option A or Option B. Describe your real share or the reported poll, make your judgment with a reason, and use this week's terms (one-proportion z interval, margin of error, percentage point, conservative p̂, sample-size formula for a proportion, undercoverage, non-response bias, question-wording bias) correctly.
2. The strongest objection (roughly 100 words). Write the best argument against your own position that you can — for example, that a large sample makes the poll trustworthy whatever its method, that the people who did not answer are probably no different, or that a margin of 3 points means the share cannot be off by more than 3 points. Argue it honestly; a weak objection you knock over earns no credit.
3. Your answer to it (roughly 100 words). Respond to that objection. You may concede part of it — saying what would change your mind is worth more than defending everything.
4. One thing you would still check (one or two sentences). What detail about who was asked, who answered, or how the question was worded would settle it?

Effort. Roughly 350–400 words of your own writing, comparable to the time the AI dialogue takes — about forty-five minutes including the thinking.

What you submit. Post those four parts, under those four labels, as your Week 12 discussion post. That post is your entire submission; this route has no share link.

No replies to classmates are required.

Participation rubric

This discussion is worth 10 points. The same three criteria score both routes.

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