Week 5 — Sleep by the Numbers: A Sleep-Science Brief — Traditional alternative (no AI)

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

Assignment 5 of the term — convert the timing of the first REM period, compute the mean of a sleep study's quiz scores, explain what each number can and cannot tell you, and tell a friend what the sleep evidence really shows.

This week you learned that consciousness runs on a continuum, that light sets the body clock, that one night cycles through NREM-1, NREM-2, NREM-3, and REM sleep, and that sleep helps consolidate memories. In Week 2 you learned that a correlation earns the words "associated with" and nothing stronger; this week you apply that habit to a claim about sleep. In this assignment you work two short problems, interpret each one, and explain to someone who has never studied psychology what the sleep evidence really shows. This week's lecture tutorial, quiz, discussion, and Analysis Workshop practise the same ideas from other angles.

The task

Two pieces of this week anchor the assignment. First, the National Institute of Neurological Disorders and Stroke reports that the first REM period comes about 90 minutes after a person falls asleep, and that most adults need about 7 to 9 hours of sleep a night. Second, in the course's illustrative dataset, ten students reported their hours of sleep the night before a quiz scored out of 20; the correlation coefficient for sleep and score is r = 0.8457. The dataset was constructed for this course to teach with; it is not from a real study.

Work these two problems, showing your arithmetic:

1. The first REM period comes about 90 minutes after a person falls asleep, according to the National Institute of Neurological Disorders and Stroke. There are 60 minutes in an hour. About how many hours after falling asleep does the first REM period arrive?
2. In the ten-student illustrative dataset, the quiz scores of the 3 students who slept fewer than 7 hours add up to 37 and the quiz scores of the 7 students who slept 7 to 9 hours add up to 110, on a quiz scored out of 20. What is the mean quiz score of all ten students?

Beside each answer, add one brief interpretation of what the number tells you and one limit of it. For problem 1, name the sleep stages that come before the first REM period in order, say which stage is the deepest and what marks REM sleep, and explain why "REM is the deepest sleep" is a mistake. For problem 2, say what r = 0.8457 shows about direction and strength, name one third variable and the directionality problem, say what kind of study could test whether sleep causes higher scores, and explain whether memory consolidation makes the claim more believable without proving it.

Explain it to a non-expert

A teammate tells you, "I read that students who sleep more get better grades, so sleep is the secret to an A — I'll sleep 9 hours before the test and I'm set." Write a 3–5 sentence message that explains, in everyday words, what a finding like this does and does not show, names one other thing that could explain it, and gives one honest reason sleep may still help. Name one limit, such as a small or made-up sample. Explain any technical term in everyday words.

For a different, ungraded example, imagine a bookstore owner who noticed that customers who come to author readings buy more books and wants to know whether the readings cause the extra sales. Model answer: "The readings and the sales go together, but that does not prove the readings cause the buying. The people who come to readings may already be your biggest readers, so they would buy more anyway. To know for sure, you would need to compare similar customers where only the readings differ. Your numbers come from one store, too, so another store might see something different."

Use that pattern for your teammate, with your own explanation and evidence.

Show your arithmetic. A reader should be able to reproduce every number you report from the values above without guessing which values or steps you used.

Deliverables

Submit a single sleep-science brief containing:

• the two answers, each with the arithmetic shown and a brief interpretation of what the number tells you and one limit of it;
• your message to the teammate, explaining in everyday words what the finding does and does not show, one other explanation, one honest reason sleep may still help, and one limit; and
• a one-line restatement of the values you used, so your results are reproducible.

Keep it to roughly one page. Clear and correct beats long.

Choose how you show it. Present your brief as written text, or as a recorded audio or video explanation of about three minutes with a transcript, or as a labelled sketch of one night's sleep cycle with a short note. 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. You may use a calculator or a spreadsheet for the arithmetic. Submitting AI-generated work as your own, or copying another student's numbers, is an integrity violation under the course policy.

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