Week 9 — How Far Does the Survey Reach? Testing a Sample and an Analogy in an Ad — Traditional alternative (no AI)
Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.
Assignment 8 of the term — check who a survey actually reached, judge a generalization as strong or weak, catch a story standing in for a trend, test a comparison, and explain to someone new why a glowing survey and a catchy comparison do not show the plan works for most people.
This week you learned to tell a population from a sample, to name the three ways a sample can mislead, to see why how a sample is chosen matters more than its size, to spot a hasty generalization from one vivid anecdote, and to test an argument from analogy. In this assignment you work four short problems on one illustrative ad, interpret each one, judge a generalization as strong or weak as Week 3 taught you, and explain to someone who has never studied critical thinking why a glowing survey is not proof. This week's lecture tutorial, quiz, discussion, and Argument Workshop practise the same ideas from other angles.
The task
Your text is an illustrative ad for a fitness app, with no real app, company, or member behind it: "Nine in ten of our members love the new workout plan! We emailed a survey to all 4,000 members, 400 replied, and 360 of them said they love it. One member finished her first marathon after three months on the plan, so it will get anyone race-ready. Using our app is like hiring a personal trainer: a trainer plans your workouts, and so does our app, so you'll get the results a trainer gets."
Work these four problems, showing your arithmetic and quoting the sentences you use:
- The ad says it emailed a survey to all 4,000 members and 400 replied. What percentage of the members replied?
- Of the 400 members who replied, 360 said they love the plan. What percentage of the replies said they love it?
- Of the 4,000 members the survey was emailed to, how many did not reply?
- Of the 400 replies, how many did not say they love the plan?
Beside each answer, add one brief interpretation:
- Problem 1: name the population and the sample the ad's first sentence is about, name the trap in how the sample came together, and explain why the members who replied might differ from those who did not.
- Problem 2: write the ad's first sentence as an inductive generalization (what was observed, and what it concludes about all members), judge it strong or weak, and say whether it could be cogent if its premise is true.
- Problem 3: name the fallacy in the marathon sentence, count how many cases it rests on, and describe the kind of evidence that would bear on whether the plan gets people race-ready.
- Problem 4: run the three-step analogy test on the personal-trainer comparison: list a similarity that bears on the conclusion, name a disanalogy, and give your verdict, then write the message to the friend described below.
Explain it to a non-expert
A friend who has never studied logic sees the ad and asks, "Nine in ten members love it and it's like having a personal trainer, so I should sign up, right?" Write a 3–5 sentence message that explains in everyday words why the survey does not show that nine in ten of all members love the plan and why the trainer comparison is not proof, reports the percentage of members who replied and how many members did not reply, and names one limit: nobody knows how the silent members feel, so the plan could be better or worse for them than the ad suggests. Explain any technical term in everyday words. More than one good answer is possible.
For a different, ungraded example, imagine a café sign that says "Our online reviewers give us top marks, so you'll love it here." Model answer: "Those reviews come only from people who chose to write one, and the happiest and the angriest customers are the most likely to bother. That makes the reviewers a self-selected group, not a fair picture of every customer. Before deciding, try to find out how many customers never left a review, or ask a few friends who have eaten there."
Use that pattern for the friend, with your own wording and evidence.
Show your arithmetic, write each trap and fallacy name out in full, and quote the sentences you use. A reader should be able to reproduce every number you report, and find every quoted sentence in the ad, without guessing which values, steps, or sentences you used.
Deliverables
Submit a single report containing:
- the four answers, each with the arithmetic shown and the brief interpretation the task names for that problem;
- your message to the friend, explaining why the survey does not show that nine in ten of all members love the plan and why the trainer comparison is not proof, reporting the percentage of members who replied and how many did not reply, and naming one limit; and
- a one-line restatement of the values you used (the members emailed, the members who replied, and the replies that said they love the plan), so your answers are reproducible.
Keep it to roughly one page. Clear and correct beats long.
Choose how you show it. Present your report as written text, or as a recorded audio or video explanation of about three minutes with a transcript, or as a labelled sketch that shows the 4,000 members, the 400 who replied, and the 360 who said they love the plan as nested groups, with a short note that says each verdict in words. Every form is graded by the same scoring criteria. Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.
How you'll be graded
The full analytic rubric is attached to this assignment in Canvas.
Academic integrity and AI use
This version is designed to be completed without AI: do the computations, the interpretations, and the writing yourself, without a chatbot or other AI tool. Quote the ad only as it is printed here, word for word. Submitting AI-generated work as your own, or copying another student's work, is an integrity violation under the course policy.
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