Week 12 Discussion — How Far Can You Trust a Share? — Traditional alternative (no AI)

Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.

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 discussion 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. Pick one you actually care about, and tell us the story.

Expectations

Activity format: one initial post followed by two substantive peer replies. Plan on about 45 minutes across the two deadlines; your instructor sets both due dates in Canvas. This version uses no AI: write your post and your replies in your own words, without a chatbot.

Your initial post — by the first due date (early in the module week):

• Say which option you chose.
• Describe your real share or the reported poll in plain words, so a reader who was not there knows what is being measured and how the sample was or would be drawn.
• Use at least two of 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.
• Give your judgment, about the margin and sample size you would plan for or about how much you trust the reported share, with a reason.
• Length: roughly 150–250 words if written. You may instead record your post as audio or video (about two minutes) and attach a transcript; both forms are scored by the same rubric.

Your replies — by the second due date (the end of the module week):

• Reply substantively to at least two classmates.
• A substantive reply does more than agree: ask whether the poster read the margin in percentage points, whether the sample size they planned really halves the margin they wanted, or which bias their margin of error would miss and which way it could push the share. "Nice point!" on its own does not count.

What a strong post looks like:

I chose Option B. The 52% comes from an online survey that readers chose to answer, so it is a voluntary-response sample. The plus-or-minus 3 points only describes how much a random sample's share would wobble, so it tells me nothing about who skipped the survey. People with strong feelings about the bus line, for or against, are the most likely to click, so the true share could be well outside 49% to 55%. Before I believed it, I would want to know how the sample was drawn and the exact wording of the question.

Notice how it names the kind of sample, reads the margin in percentage points, keeps sampling variability apart from bias, and says what it would check. That is the bar.

Participation rubric

This discussion is worth 10 points. The three criteria below look at your initial post and your peer replies.

Post early if you can — the best threads happen when people have time to reply before the second due date.

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