Week 13 — Quiz (auto-graded) · Hypothesis Testing: Foundations

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Objective tested: Objective 7 — conduct and interpret hypothesis tests (the logic: H₀/Hₐ, p-value vs. α, Type I/II, significance).
Points: 10 (1 each) · Assignment group: Quizzes (15% of grade) · Due: end of Module 13 (Sun Nov 29, extended past Thanksgiving).

This is the human-readable quiz with its vetted answer key and feedback. The import-ready Classic QTI is in F-quiz-week-13-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 13 misconceptions named in the lecture outline. This is a conceptual week — any number in a stem is supplied; nothing must be computed.

Questions, key, and feedback

Q1 (MC). A bakery's cupcakes have long averaged 120 calories. A nutritionist suspects the recipe changed and the average is now different. For a hypothesis test, what is the null hypothesis (H₀)?
- A. μ = 120 calories ✅
- B. μ ≠ 120 calories
- C. μ > 120 calories
- D. The nutritionist's suspicion is correct
Feedback: H₀ is the "no change / status quo" claim and always carries the equals idea — the mean is still 120. The nutritionist's suspicion is the alternative. (B–D drop the "=", which H₀ must keep.)

Q2 (MC). A tutoring company claims its program raises students' average test score above the school average of 75. You want to test that claim. The correct alternative hypothesis (Hₐ) is —
- A. μ = 75
- B. μ ≠ 75
- C. μ > 75 ✅
- D. μ < 75
Feedback: The claim is one-directional ("above 75"), so Hₐ: μ > 75. H₀ would be μ = 75. (Hₐ never gets an "="; "above" points only up.)

Q3 (MC). Which statement best describes what a p-value is?
- A. The probability that the null hypothesis is true
- B. The probability of getting data at least as extreme as observed, assuming H₀ is true ✅
- C. The probability that the alternative hypothesis is true
- D. The size of the effect the study found
Feedback: The p-value measures how surprising the data would be if H₀ were true. (A is the #1 classic misreading; D confuses significance with effect size.)

Q4 (MC). A test is conducted at significance level α = 0.05, and the data produce p = 0.02. What is the correct decision?
- A. Reject H₀ ✅
- B. Fail to reject H₀
- C. Accept H₀ as proven true
- D. Increase α until the result changes
Feedback: The rule is p ≤ α → reject H₀, and 0.02 ≤ 0.05. A test never "accepts H₀ as proven," and α is fixed before seeing the data. (C and D are both classic errors.)

Q5 (MC). A study tests H₀: μ = 8 hours of sleep vs. Hₐ: μ < 8 for college students, sets α = 0.05, and finds p = 0.01, leading to rejecting H₀. Which is the best conclusion in context?
- A. We proved college students sleep exactly 8 hours
- B. At the 0.05 level, there is significant evidence that the mean sleep is less than 8 hours ✅
- C. There is a 1% chance the null hypothesis is true
- D. The effect is large and important
Feedback: A good conclusion restates the real-world claim at the stated α — not just "reject H₀." (C misreads the p-value; D confuses "significant" with "large.")

Q6 (True / False). "A p-value of 0.04 means there is a 4% probability that the null hypothesis is true."
- True
- False ✅
Feedback: False. The p-value is computed assuming H₀ is true, so it can't be the probability H₀ is true. The p-value assumes the null, so it can't measure the null.

Q7 (True / False). "When a test results in 'fail to reject H₀,' it proves that H₀ is true."
- True
- False ✅
Feedback: False. "Fail to reject" is the jury's "not guilty," not "innocent" — there wasn't enough evidence (maybe no effect, maybe too small a sample). We never accept H₀; we just fail to reject it.

Q8 (Multiple answer — select all that apply). A study of 60,000 people finds a new app increases daily water intake by an average of 2 milliliters, and the result is statistically significant (p = 0.001). Which statements are correct?
- A. The effect is probably real (not just chance) ✅
- B. The effect must be large and important because it is statistically significant
- C. A 2-mL daily increase is likely not practically significant ✅
- D. A very large sample can make a tiny effect statistically significant ✅
- E. The p-value of 0.001 means there is a 0.1% chance the null is true
Feedback: Significant means probably real, not big (A, C, D). B confuses statistical with practical significance; E misreads the p-value. (Classic "significant ≠ important" trap.)

Q9 (MC). A spam filter uses H₀: "this email is NOT spam." The filter rejects H₀ for an email that is actually not spam — sending a legitimate email to the spam folder. This is a —
- A. Type I error ✅
- B. Type II error
- C. Correct decision
- D. Practical-significance error
Feedback: Rejecting a true H₀ is a Type I error (false positive) — a false alarm, like convicting the innocent. A Type II error would be letting actual spam through (failing to reject a false H₀).

Q10 (Matching). Match each term to its correct description.
| Term | Correct description |
|---|---|
| Type I error | Rejecting H₀ when it is actually true (false positive) |
| Type II error | Failing to reject H₀ when it is actually false (false negative) |
| Significance level α | The probability of a Type I error, set before the data |
| p-value | How surprising the data are if H₀ is true |
Feedback: Type I = false alarm (convict the innocent); Type II = a miss (free the guilty); α is the Type I rate chosen in advance; the p-value is computed under H₀.

Answer key (quick reference)

Quality gate (self-checked): each single-answer item has exactly one correct option; the multiple-answer item (Q8) lists the three correct statements (A, C, D) and excludes the two misreadings (B, E); the matching item pairs four distinct terms with four distinct descriptions. No item asserts a fact outside the Week 13 course definitions. Every numeric value (120, 75, 8, 2 mL, p = 0.02/0.01/0.04/0.001, α = 0.05) is supplied in the stem — no computation, so nothing to mis-key. The decision-rule items use friendly pre-decided comparisons (0.02 ≤ 0.05 → reject; 0.01 ≤ 0.05 → reject).

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

All ten items are tagged course=MATH11 · week=13 · objective=7 · topic=hypothesis-testing-foundations and deposited in Item Bank: Week 13 — Hypothesis Testing: Foundations. The final (Week 16) and the per-term variant updates draw fresh items from this bank. (Tags: q1 null-hypothesis, q2 alternative-hypothesis, q3 p-value-definition, q4 decision-rule, q5 conclusion-in-context, q6 misread-pvalue, q7 misread-fail-to-reject, q8 statistical-vs-practical, q9 type-I-error, q10 errors-matching.)

Canvas placement block

canvas_object   = Quizzes::Quiz
title           = "Week 13 Quiz — Hypothesis Testing: Foundations"
assignment_group = "Quizzes"
points_possible = 10
grading_type    = points
due_offset_days = 7        # Sun Nov 29 — extended past Thanksgiving (module starts Tue Nov 24)
published       = true
shuffle_answers = true
provenance      = "~ Prof. Rivera's edition · Fall 2026 · built with thecoursemaker.com"