Week 13 Discussion — How Sure Is Sure Enough? — Traditional alternative (no AI)

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

Hook

A student says they guessed on every question of a 10-question quiz with four options per question, and they scored 7. This week you tested that claim. If the student were purely guessing, a score of 7 or more would occur on about 35 quizzes in 10,000, a p-value of 0.0035, so at a significance level of α = 0.05 you reject H₀. That arithmetic is the easy part. Every test also carries two judgments that no formula makes for you: how much risk of a false alarm you will accept, and whether a "significant" result is big enough to matter.

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 real yes-or-no decision made under uncertainty in your life, your major, your job, or your community, such as a smoke alarm, a medical screening test, a spam filter, a safety check on a product, or a jury verdict. Say what the null hypothesis would be there, and what a Type I error and a Type II error would each look like. Then argue which of the two errors is worse in that setting, and whether you would set the significance level at 0.05, stricter, or looser. Use the guessing quiz as your reference: the rule "reject when the score is 5 or more" wrongly flags a pure guesser with probability 0.0781, the stricter rule "7 or more" does so with probability 0.0035, and the stricter rule misses more students who really do know some of the material.

Option B: Take a position on this claim: "If a study's p-value is below 0.05, its result matters and people should act on it." Start from the guessing quiz: a score of 4 out of 10 (40%) has a p-value of 0.2241, while a score of 40 out of 100 on a 100-question version, the same 40%, sits about 3.46 standard deviations above the guessing mean of 25 and has a p-value well below 0.01. Then bring in a setting from your major or your work, such as a new study method, a medicine, a change to a store's prices, or a training program, and argue when a small p-value should and should not change a real decision. Along the way, say in your own words what a p-value does and does not tell you.

There is no single right answer. A smoke alarm, a cancer screening, and a jury can each be argued well in more than one direction, and reasonable people weigh a modest but real edge differently in medicine, business, and education. Pick a setting 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.

AI use. This discussion is done without a chatbot. Your post and your replies are your own reasoning in your own words, and every number you use comes from this week's materials or a source you name.

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

• Say which option you chose.
• Describe your real decision or study claim in plain words, so a reader who was not there knows what is being decided and what is at stake.
• Use at least two of this week's terms (null hypothesis, alternative hypothesis, test statistic, p-value, significance level, Type I error, Type II error, power, statistically significant, practical significance) correctly.
• Give your position with a reason, and name the cost, the trade-off, or the size of effect your reason rests on.
• 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 matched each error type to the right outcome, test whether their reading of a p-value treats it as the chance that H₀ is true, or ask what size of effect would change their verdict. "Nice point!" on its own does not count.

What a strong post looks like:

I chose Option A. At my job on a food-packing line, a metal detector checks every package. The null hypothesis is the "nothing is wrong" claim: this package is clean. A Type I error stops a clean package, and a Type II error lets a package with metal in it reach a customer. I think the Type II error is far worse here, so I would accept more false alarms, a looser α, to miss fewer real problems. That is the same trade the guessing quiz shows between the cutoffs of 5 and 7, run in the other direction.

Notice how it states the null hypothesis, matches each error to a real outcome, weighs the two costs with a reason, and uses the week's terms precisely. 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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