Midterm Practice Exam (ungraded) · Weeks 1–7 (Objectives 1–4)

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
What this is: a low-stakes rehearsal for the cumulative midterm. It mirrors the real exam's blueprint — same coverage, item-type mix, length, and application-skewed difficulty — but is built from fresh item-bank variants and shares none of the live midterm's questions.
Settings: ungraded (0 points) · unlimited attempts · feedback shown after submission · opens before the exam window so you can prepare.

This is the human-readable practice exam with its vetted answer key and feedback (released after submission). The import-ready Classic QTI 1.2 is in O-practice-exam-week-08-qti.xml (generated by a validated Python script — parses with 20 items). The Canvas placement block is at the bottom.

Integrity note for students. Every item here is a fresh variant — new numbers and contexts — with a pre-computed, vetted answer. None of these are the live midterm questions. Working them builds the skill the midterm tests, honestly. The paired live exam is L-midterm-week-08.md.

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Blueprint (mirrors the midterm)

Coverage is proportional to teaching time, matching the real exam: Obj 1 ≈ 4 · Obj 2 ≈ 5 · Obj 3 ≈ 3 · Obj 4 ≈ 8. (The actual midterm items are not listed here — only the shared structure.)

#	Type	Concept	Objective	Week
1	Multiple choice	Population vs. sample (identify the population)	1	1
2	Multiple choice	Parameter vs. statistic	1	1
3	Multiple choice	Level of measurement — ratio	1	1
4	Multiple choice	Sampling bias (voluntary response)	1	1
5	Multiple choice	Relative frequency from a table	2	2
6	Multiple choice	Outlier's effect on mean vs. median	2	2–3
7	Multiple choice	Compute the mean	2	3
8	Multiple choice	IQR from a five-number summary	2	3
9	Multiple choice	What standard deviation measures (spread, not center)	2	3
10	Multiple answer	True statements about correlation r	3	4
11	Multiple choice	Marginal proportion (two-way table)	3	4
12	Multiple choice	Explanatory vs. response (which axis)	3	4
13	Multiple choice	Basic probability from a sample space	4	5
14	Multiple choice	Addition rule (mutually exclusive)	4	5
15	Multiple choice	Conditional probability (two-way table)	4	5
16	True / False	Gambler's-fallacy misconception	4	5
17	Multiple choice	Expected value with a negative outcome	4	6
18	Multiple choice	Identify a valid probability distribution	4	6
19	Multiple choice	Binomial mean (np)	4	7
20	Multiple choice	When the normal approximation applies	4	7

Objective totals: Obj 1 = 4 · Obj 2 = 5 · Obj 3 = 3 · Obj 4 = 8 → 20 items (ungraded; mirrors the 100-point midterm's emphasis).

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Questions, key, and feedback (feedback releases after you submit)

Objective 1 — Foundations & Types of Data (Week 1)

Q1 (MC). A streaming service wants to know the average number of hours per week that all 9,000 subscribers in a city spend watching. It examines viewing logs for a randomly selected 250 subscribers. What is the population?
- A. The 250 subscribers whose logs were examined
- B. All 9,000 subscribers in the city ✅
- C. The average number of hours watched
- D. Subscribers who watch every day
Feedback: The population is everyone the question is about — all 9,000 subscribers. The 250 examined are the sample.

Q2 (MC). A researcher measures a random sample of 60 newborns at a hospital and finds their average birth weight is 7.4 pounds. The value 7.4 pounds is best described as a —
- A. Parameter
- B. Statistic ✅
- C. Population
- D. Census
Feedback: It's computed from a sample (60 newborns), so it's a statistic. The matching figure for all newborns would be a parameter.

Q3 (MC). Which of the following variables is measured at the ratio level (equal gaps and a true zero)?
- A. Temperature in degrees Celsius
- B. A hotel's star rating (1 to 5 stars)
- C. The number of emails a person received today ✅
- D. A jersey number on a team roster
Feedback: A count of emails has a true zero (0 = none) and equal gaps → ratio. Celsius is interval (no true zero), star rating is ordinal, and a jersey number is nominal.

Q4 (MC). A morning radio show invites listeners to call in and answer "Should the city build a new sports arena?" Over 5,000 people call. The results are most threatened by —
- A. Voluntary-response bias ✅
- B. It is a census of all city residents
- C. It is a simple random sample
- D. No bias, because 5,000 is a large number
Feedback: Callers opt in and radio listeners aren't typical residents — voluntary-response bias. A large count doesn't fix a biased method.

Objective 2 — Summarizing Data (Weeks 2–3)

Q5 (MC). A clinic records the number of visits in a year for 50 patients, grouped: 0–1 visits → 8 patients; 2–3 → 22; 4–5 → 14; 6 or more → 6. What share of patients had 4 or more visits?
- A. 12%
- B. 28%
- C. 40% ✅
- D. 60%
Feedback: Relative frequency = count ÷ total. 4-or-more = 14 + 6 = 20 patients; 20 ÷ 50 = 0.40 = 40%.

Q6 (MC). Seven employees' years of service are 3, 4, 5, 6, 7, 8, 9 (mean 6, median 6). A data-entry error changes the 9 to 79. What happens to the mean and the median?
- A. Both the mean and the median jump up a lot
- B. The mean jumps up a lot (to 16), but the median stays 6 ✅
- C. The median jumps a lot, but the mean stays 6
- D. Neither the mean nor the median changes
Feedback: The mean uses every value, so it climbs from 6 to 16 (new sum 112 ÷ 7); the median depends only on position, so it stays 6. The median is resistant; the mean is not.

Q7 (MC). A student's six homework scores are 7, 9, 10, 8, 6, 14. What is the mean score?
- A. 8.5
- B. 9 ✅
- C. 9.5
- D. 54
Feedback: Add them (7+9+10+8+6+14 = 54) and divide by the count (6): 54 ÷ 6 = 9. The total, 54, is distractor D.

Q8 (MC). Daily step counts (in thousands) have the five-number summary Min = 2, Q1 = 5, Median = 8, Q3 = 11, Max = 20. What is the interquartile range (IQR)?
- A. 18
- B. 6 ✅
- C. 3
- D. 9
Feedback: IQR = Q3 − Q1 = 11 − 5 = 6 (the spread of the middle 50%). The range, Max − Min = 18, is the classic distractor.

Q9 (MC). Two classes take the same exam and have the same mean score, but Class A's scores are tightly clustered while Class B's are widely scattered. Which statement is correct?
- A. Class A has the larger standard deviation
- B. Class B has the larger standard deviation ✅
- C. The two classes must have the same standard deviation because their means are equal
- D. Standard deviation cannot be compared unless the means differ
Feedback: Standard deviation measures spread around the mean, not the center. The more scattered class (B) has the larger SD even though the means match.

Objective 3 — Exploring Relationships (Week 4)

Q10 (Multiple answer — select all that apply). Select all statements about the correlation coefficient r that are true.
- A. r is always between −1 and +1 ✅
- B. r has units, such as dollars or hours
- C. r measures the direction and strength of a linear relationship ✅
- D. r = 0.7 means "70% of a perfect relationship"
- E. A correlation of r = 0 means there is no linear relationship ✅
Feedback: r is a unitless number from −1 to +1 measuring linear direction and strength; r = 0 means no linear pattern. r has no units (B) and isn't a percentage (D).

Q11 (MC). A survey of 400 shoppers records membership status and coupon use. Of all 400 shoppers, 100 used a coupon. The value 100 / 400 = 0.25 (the share of all shoppers who used a coupon) is an example of a —
- A. Conditional proportion
- B. Marginal proportion ✅
- C. Cell count
- D. Correlation
Feedback: It uses the grand total (400) as the denominator and describes one variable overall — a marginal proportion. A conditional proportion would divide by one group's total.

Q12 (MC). An economist wants to use the hours students study per week to help explain their final exam scores. In a scatterplot, which variable belongs on the x-axis?
- A. Hours studied per week ✅
- B. Final exam score
- 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 (exam score) goes on y. "x explains, y responds."

Objective 4 — Probability & Random Variables (Weeks 5–7)

Q13 (MC). You roll one fair six-sided die. What is the probability of rolling a number greater than 4 (that is, a 5 or a 6)?
- A. 1/6
- B. 1/3 ✅
- C. 1/2
- D. 2/3
Feedback: Favorable outcomes are 5 and 6 (2 of the 6 faces): 2 ÷ 6 = 1/3.

Q14 (MC). A bag holds 4 red, 5 blue, and 6 green marbles (15 total). You draw one marble. What is the probability it is red or green? (A marble can't be two colors.)
- A. 4/15
- B. 6/15
- C. 10/15 ✅
- D. 1/15
Feedback: Red and green are mutually exclusive, so add: 4/15 + 6/15 = 10/15 (= 2/3). No overlap to subtract.

Q15 (MC). A two-way table of 250 students classifies them by on-campus residence and bicycle ownership. Of the 90 students who live on campus, 36 own a bicycle. What is P(owns a bicycle | lives on campus)?
- A. 36 / 250 = 0.144
- B. 90 / 250 = 0.36
- C. 36 / 90 = 0.40 ✅
- D. 54 / 90 = 0.60
Feedback: "Given lives on campus" restricts you to those 90 students; 36 own a bicycle, so 36 ÷ 90 = 0.40.

Q16 (True / False). A fair six-sided die has come up a 6 on each of the last four rolls. Therefore a 6 is less likely than usual on the next roll.
- True
- False ✅
Feedback: False. Independent rolls have no memory — the next roll still gives each face probability 1/6. Believing otherwise is the gambler's fallacy.

Q17 (MC). A charity raffle sells tickets. For a ticket buyer, the net gain X is +$90 with probability 0.05 (you win the prize) and −$10 with probability 0.95 (you don't win, losing the ticket cost). What is the expected net gain E(X)?
- A. −$5 ✅
- B. $0
- C. +$4.50
- D. +$40
Feedback: E(X) = (90)(0.05) + (−10)(0.95) = 4.50 − 9.50 = −$5. On average a buyer loses $5 per ticket — the charity's edge. Expected values can be negative.

Q18 (MC). A discrete random variable has four possible values. Which set of probabilities forms a valid probability distribution?
- A. 0.4, 0.3, 0.2, 0.2
- B. 0.5, 0.3, 0.1, 0.1 ✅
- C. 0.6, 0.5, −0.2, 0.1
- D. 0.3, 0.3, 0.3, 0.3
Feedback: B's probabilities are each in [0, 1] and sum to exactly 1 (0.5 + 0.3 + 0.1 + 0.1 = 1.0). A and D sum to 1.1 and 1.2; C contains a negative probability.

Q19 (MC). A free-throw shooter makes 80% of her attempts. She takes 25 independent attempts, so the number made X ~ Binomial(n = 25, p = 0.8). What is the expected number she makes? (Mean = np.)
- A. 5
- B. 20 ✅
- C. 12.5
- D. 25
Feedback: Mean = np = 25 × 0.8 = 20. (Using the miss probability, 25 × 0.2 = 5, is distractor A.)

Q20 (MC). The normal approximation to the binomial may be used only when np ≥ 10 AND n(1 − p) ≥ 10. For which of the following is the normal approximation NOT appropriate?
- A. n = 40, p = 0.5
- B. n = 200, p = 0.5
- C. n = 25, p = 0.04 ✅
- D. n = 60, p = 0.3
Feedback: For C, np = 25 × 0.04 = 1, far below 10 → fails; use the exact binomial. (A: 20 & 20; B: 100 & 100; D: 18 & 42 all pass.)

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Answer key (quick reference)

Q	Answer	Q	Answer
1	B	11	B
2	B	12	A
3	C	13	B (1/3)
4	A	14	C (10/15)
5	C (40%)	15	C (36/90 = 0.40)
6	B	16	False
7	B (9)	17	A (−$5)
8	B (6)	18	B
9	B	19	B (20)
10	A, C, E	20	C

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Quality gate (H5 — self-checked, computer-verified)

• Mirror check: 20 items, coverage Obj 1 = 4 · Obj 2 = 5 · Obj 3 = 3 · Obj 4 = 8 — matches the midterm blueprint's emphasis and item-type mix.
• Single-answer integrity: every multiple-choice and true/false item (Q1–Q9, Q11–Q20) has exactly one correct option; the multiple-answer item (Q10) keys A, C, E (B and D must be left unselected).
• Arithmetic pre-computed and independently re-verified (Python verify_arithmetic.py): Q5 20/50 = 0.40; Q6 new mean 112/7 = 16 (median unchanged at 6); Q7 54/6 = 9; Q8 IQR 11−5 = 6; Q13 2/6 = 1/3; Q14 (4+6)/15 = 10/15; Q15 36/90 = 0.40; Q17 (90)(0.05)+(−10)(0.95) = −5; Q18 valid set sums to 1.0; Q19 25×0.8 = 20; Q20 fails only for np = 25×0.04 = 1. All checks PASS.
• QTI parse confirmation: O-practice-exam-week-08-qti.xml parses as imsqti_xmlv1p2 with 20 items; every single-answer respcondition sets SCORE = 100 on exactly one option. (In Canvas the placement makes it ungraded with feedback on; the engine still scores attempts so students see what they missed.)
• Integrity vs. the live exam: 0 items are shared with L-midterm-week-08.md — verified by full stem-plus-options comparison. Where a concept slot overlaps the midterm, this form uses different numbers and contexts (e.g., midterm Q7 is a median; here Q7 is a mean; midterm Q8 IQR uses quiz scores 12/28/35/44/60 → 16, here step counts 2/5/8/11/20 → 6).
• No content outside the Weeks 1–7 course definitions; no hallucinated facts.

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Item-bank & coverage note

All 20 items are fresh variants assembled from the Week 1–7 item banks per Prompt O, preferring items not used on the live midterm and authoring fresh variants where a concept overlaps. Tagged course=MATH11 · form=practice-midterm · weeks=1–7 · objectives=1–4 and deposited back into the banks for future per-term ($39) regenerations. Each term's update regenerates fresh practice variants alongside the midterm and continues to share none of the live items.

Canvas placement block

canvas_object             = Quizzes::Quiz
title                     = "Midterm Practice Exam (ungraded)"
assignment_group          = "Practice exercises"
points_possible           = 0
grading_type              = not_graded
allowed_attempts          = unlimited
show_feedback             = true        # released after submission
available_from_offset_days = -3        # opens 3 days before the exam window
due_offset_days           = 6         # on or before the exam due date
published                 = true
shuffle_answers           = true
provenance                = "~ Prof. Rivera's edition · Fall 2026 · built with thecoursemaker.com"