Week 4 — Quiz (auto-graded) · Exploring Relationships

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Objective tested: Objective 3 — describe the relationship between two variables (scatterplots, correlation, two-way tables, lurking variables).
Points: 10 (1 each) · Assignment group: Quizzes (15% of grade) · Due: end of Module 4.

This is the human-readable quiz with its vetted answer key and feedback. The import-ready Classic QTI is in F-quiz-week-04-qti.xml; the reusable item-bank entries and the Canvas placement block are at the bottom of this file.

Blueprint

No trick questions; distractors target the Week 4 misconceptions named in the lecture outline. All arithmetic is pre-computed.

Questions, key, and feedback

Q1 (MC). A researcher wants to use a student's hours of sleep to help explain their reaction time on a test. In a scatterplot, which variable belongs on the x-axis?
- A. Hours of sleep ✅
- B. Reaction time
- C. Either one — it makes no difference
- D. The student's ID number
Feedback: The explanatory variable (the one doing the explaining) goes on the x-axis; the response goes on y. "x explains, y responds."

Q2 (MC). In a scatterplot, as the outdoor temperature rises, the amount of heating oil a home uses falls, with the points lying close to a straight line. The relationship's direction is —
- A. Positive
- B. Negative ✅
- C. No direction
- D. Curved
Feedback: As x goes up, y goes down — the dots fall left-to-right — so the direction is negative.

Q3 (Multiple answer — select all that apply). Which of the following statements about the correlation coefficient r are true?
- A. r is always between −1 and +1 ✅
- B. r has units (for example, hours or dollars)
- C. A correlation of r = 0 means there is no linear relationship ✅
- D. r = 0.6 means "60% of a perfect relationship"
- E. r measures the direction and strength of a linear relationship ✅
Feedback: r is a unitless number on −1 to +1 that measures linear direction and strength; r = 0 means no linear pattern. r has no units (B) and is not a percent (D). (B and D are the named traps.)

Q4 (MC). Two variables have a correlation of r = −0.85. The best description is —
- A. A weak negative relationship
- B. A strong, negative, linear relationship ✅
- C. A strong, positive, linear relationship
- D. No relationship
Feedback: The size (0.85, close to 1) means strong; the minus sign means negative. So: strong, negative, linear.

Q5 (True / False). "If the correlation between two variables is r = 0, then the two variables have no relationship of any kind."
- True
- False ✅
Feedback: False. r = 0 means no linear relationship — the variables can still be strongly related in a curve (e.g., a U-shape). Always look at the scatterplot.

Q6 (Matching). Match each correlation value to the scatterplot it best describes.
| Correlation | Correct description |
|---|---|
| r ≈ +0.95 | Points rise tightly along a straight line (strong positive) |
| r ≈ −0.95 | Points fall tightly along a straight line (strong negative) |
| r ≈ +0.30 | Points drift upward in a loose, scattered cloud (weak positive) |
| r ≈ 0 | A shapeless blob with no straight-line trend |
Feedback: Sign sets the direction (up vs. down); size sets the tightness (near ±1 is tight, near 0 is loose/none).

Q7 (MC). A survey of 250 students recorded whether each drinks coffee daily and whether each is a "morning person":

Among the students who drink coffee daily, what proportion are morning people?
- A. 96 / 250 = 38.4%
- B. 96 / 150 = 64% ✅
- C. 40 / 100 = 40%
- D. 54 / 150 = 36%
Feedback: "Among coffee drinkers" is a conditional proportion — divide by the coffee-daily row total (150), not the grand total: 96 / 150 = 64%. (A uses the wrong denominator.)

Q8 (MC). Using the same table, the value 150 / 250 = 60% (the proportion of all students who drink coffee daily) is an example of a —
- A. Marginal proportion ✅
- B. Conditional proportion
- C. Cell count
- D. Correlation
Feedback: It describes one variable using the grand total (250) as the denominator — that's a marginal proportion. A conditional proportion would divide by one group's total instead.

Q9 (True / False). "Researchers found a strong positive correlation between the number of hours people spend on social media and their anxiety levels (an observational survey). This proves that social media causes anxiety."
- True
- False ✅
Feedback: False. A strong correlation from an observational study is a link, not proof of cause — a lurking variable could drive both, and nothing was randomly assigned. Correlation ≠ causation.

Q10 (MC). A study reports that towns with more churches tend to have more bar fights, and a columnist concludes churches cause crime. The most likely lurking variable is —
- A. The number of churches
- B. The number of bar fights
- C. The town's population size ✅
- D. There is no lurking variable; churches cause crime
Feedback: Bigger towns have more of everything — more churches and more bar fights. Population size drives both, so the correlation isn't causal. Ask who else is in the room.

Answer key (quick reference)

Quality gate (self-checked): each single-answer item has exactly one correct option; the multiple-answer item (Q3) lists the three true statements (A, C, E) and excludes the two named traps (B units, D percent). All arithmetic is pre-computed and verified: Q7 conditional 96 / 150 = 0.64 = 64% (distractor A = 96 / 250 = 38.4%, the wrong denominator); Q8 marginal 150 / 250 = 60%. No item asserts a fact outside the Week 4 course definitions.

Item-bank entries (for variants + the midterm/final)

All ten items are tagged course=MATH11 · week=4 · objective=3 · topic=exploring-relationships and deposited in Item Bank: Week 4 — Exploring Relationships. The midterm (Week 8) and the per-term variant updates draw fresh items from this bank. (Tags: q1 explanatory-response, q2 scatterplot-direction, q3 correlation-properties, q4 interpret-r, q5 r-zero-misconception, q6 match-r-scatter, q7 conditional-proportion, q8 marginal-vs-conditional, q9 causation-misconception, q10 lurking-variable.)

Canvas placement block

canvas_object   = Quizzes::Quiz
title           = "Week 4 Quiz — Exploring Relationships"
assignment_group = "Quizzes"
points_possible = 10
grading_type    = points
due_offset_days = 6        # 6 days after module start
published       = true
shuffle_answers = true
provenance      = "~ Prof. Rivera's edition · Fall 2026 · built with thecoursemaker.com"