Week 9 — Midterm Practice Exam (unlimited attempts) · Weeks 1–8

Course: Introduction to Statistics (18-week generic edition)
Coverage: the same Weeks 1–8 map as the real midterm, at half length.
Points: 25 (25 questions × 1 point) · Assignment group: Practice exercises (0% of grade — ungraded rehearsal) · Attempts: unlimited, with feedback after every submission · Available: from the start of Week 9; finish at least one attempt before you sit the midterm.
Format: 21 multiple choice · 2 true/false · 1 multiple answer · 1 matching — the same item-type mix and week-by-week coverage shape as the live exam.

Read this first. The practice exam shares ZERO items with the real exam — it practices the same skills, not the same questions. Memorizing these answers earns you nothing on the midterm; rehearsing the moves (classify, compute, interpret) earns you everything. Take it closed-book first, like the real thing. Then use the feedback: every miss names the move to re-drill, and the exam-prep tutorial will drill it with you. Retake until a clean run feels routine — attempts are unlimited and cost nothing.

---

Blueprint

The table shows the coverage — about three items per week of the midterm's scope, plus one synthesis item, mirroring the live blueprint at half scale.

Week	Items	Concepts practiced
1	Q1–Q3	statistic vs. parameter · NOIR levels · convenience sampling & bias
2	Q4–Q6	relative frequency · skew direction · truncated axes (T/F)
3	Q7–Q9	mean vs. median · computing s · z-scores
4	Q10–Q12	describing association · conditional percents · lurking variables
5	Q13–Q15	complement rule · general addition rule · conditional probability
6	Q16–Q18	legitimate distributions · E(X) · legitimacy rules (multi)
7	Q19–Q21	binomial parameters · at least one · binomial mean & SD
8	Q22–Q25	empirical rule · forward normal · rule-needs-the-bell (T/F) · choose-the-tool synthesis (matching)

---

Questions, key, and feedback

Q1 (MC). Rangers randomly sample 150 of a park's 9,000 camping permits from last season and find that the sampled stays average 2.8 nights. The number 2.8 is —
- A. A parameter
- B. A census
- C. A statistic ✅
- D. A population
Feedback: It was computed from the sample of 150 permits, so it's a statistic; the all-permit average would be the parameter.

Q2 (MC). A farm stand's ledger records each sale's payment type (cash / card), the customer's loyalty tier (bronze / silver / gold), and the sale amount in dollars. In order, these variables are measured at the —
- A. Nominal, ordinal, and ratio levels ✅
- B. Nominal, nominal, and interval levels
- C. Ordinal, ordinal, and ratio levels
- D. Ratio, interval, and nominal levels
Feedback: Payment type just names (nominal); the tiers are ordered with unequal gaps (ordinal); dollars have a true zero (ratio).

Q3 (MC). To estimate how often residents use its new dog park, a city interviews people who are already at the dog park one afternoon. The main problem is —
- A. The interviews form a complete census of everyone who uses the park
- B. Afternoon interviews create response bias through leading wording
- C. This is cluster sampling and simply needs a few more clusters
- D. The sample is convenient but biased — frequent visitors are overrepresented ✅
Feedback: Sampling at the park guarantees you meet park-goers. Convenience isn't chance, and no interview count fixes the lean.

Q4 (MC). Of 80 hotel check-ins one evening, 24 were mobile self-check-ins. The relative frequency of mobile self-check-ins is —
- A. 0.24
- B. 0.30 ✅
- C. 0.70
- D. 24
Feedback: Count ÷ total = 24 ÷ 80 = 0.30. (0.24 misreads the count as the share; 24 is the raw count.)

Q5 (MC). Most waits at a car wash run 5 to 15 minutes, but on busy mornings a few stretch past 45 minutes. The distribution of wait times is —
- A. Skewed to the right — the long thin tail points toward the large values ✅
- B. Skewed to the left — the tall peak sits at the short waits
- C. Symmetric — most of the waits land close to one another
- D. Uniform — a wait can land anywhere between 5 and 45 minutes
Feedback: Name the shape for the tail: a few long waits stretch the tail right, so the distribution is right-skewed.

Q6 (True / False). True or False: Because a truncated frequency axis only trims empty space, it never changes the story a bar chart tells.
- True
- False ✅
Feedback: False — starting bars above zero stretches small gaps into dramatic ones. Bars start at zero; if you zoom, label it loudly.

Q7 (MC). Five escape-room teams finished in 40, 44, 46, 50, and 95 minutes. The mean and median finish times are —
- A. Mean 46 and median 55 minutes
- B. Mean 55 and median 45 minutes
- C. Mean 46 and median 50 minutes
- D. Mean 55 and median 46 minutes ✅
Feedback: Sum 275 ÷ 5 = 55; the sorted middle value is 46. One 95-minute epic drags the mean, not the median.

Q8 (MC). A concession stand's daily hot-dog counts over five days are 21, 21, 25, 29, 29, with mean 25. The sample standard deviation is —
- A. 2 hot dogs
- B. 16 hot dogs
- C. 4 hot dogs ✅
- D. 8 hot dogs
Feedback: Deviations −4, −4, 0, 4, 4 → squares total 64 → 64 ÷ 4 = 16 → √16 = 4. (16 is the variance; 8 is the range.)

Q9 (MC). Dogs' visit lengths at one park average 40 minutes with a standard deviation of 15 minutes. One dog stayed 70 minutes. The z-score for that visit is —
- A. 2.0 ✅
- B. −2.0
- C. 0.5
- D. 30
Feedback: z = (70 − 40) ÷ 15 = 2.0 — two standard deviations above the mean visit length.

Q10 (MC). A nursery's scatterplot of 45 potted trees shows taller trees selling at higher prices, with the dots loosely following an uphill line. The association is —
- A. Positive, roughly linear, and moderate ✅
- B. Negative, roughly linear, and strong
- C. Positive, clearly curved, and weak
- D. Absent, because the dots do not fall exactly on one line
Feedback: Uphill = positive; a line-like cloud = linear; "loosely" = moderate strength. Real data never sit exactly on the line.

Q11 (MC). Of 120 matinee tickets at a theater, 30 included a concession combo; of 60 evening tickets, 24 included a combo. The percent of evening tickets that included a combo is —
- A. 13%
- B. 40% ✅
- C. 30%
- D. 44%
Feedback: "Among evening tickets" → 24 ÷ 60 = 40%. (13% divides by all 180 tickets; 44% divides by the 54 combo buyers.)

Q12 (MC). Cities with more hotel rooms also record more escape-room businesses. The safest conclusion is —
- A. Building hotels causes escape rooms to open nearby
- B. Escape rooms cause hotel construction to accelerate
- C. The two are associated; a third variable such as tourism volume could drive both ✅
- D. With enough cities measured, the link would finally prove causation
Feedback: Tourist traffic plausibly builds both. Correlation is a handshake, not a push — and more data never turns a handshake into one.

Q13 (MC). A farm stand's ledger shows the probability that a customer pays cash is 0.35. The probability that a randomly chosen customer does NOT pay cash is —
- A. 0.35
- B. 0.65 ✅
- C. 0.70
- D. 1.35
Feedback: P(not A) = 1 − 0.35 = 0.65. (1.35 breaks the 0-to-1 scale — an instant upstream-error alarm.)

Q14 (MC). At an arcade, 30% of visitors play the racing game, 25% play the rhythm game, and 10% play both. The probability that a visitor plays the racing game or the rhythm game (or both) is —
- A. 0.45 ✅
- B. 0.55
- C. 0.65
- D. 0.075
Feedback: 0.30 + 0.25 − 0.10 = 0.45 — subtract the overlap so both-game players count once. (0.55 forgets the subtraction.)

Q15 (MC). Of a hotel's 60 weekday check-ins, 12 requested late checkout; of its 40 weekend check-ins, 18 requested late checkout. P(late checkout | weekend check-in) is —
- A. 0.45 ✅
- B. 0.60
- C. 0.18
- D. 0.30
Feedback: The "given" world is the 40 weekend check-ins: 18 ÷ 40 = 0.45. (0.18 divides by all 100; 0.60 answers the flipped question.)

Q16 (MC). Let X = the number of vehicles on one camping permit, where P(1) = 0.55, P(2) = 0.30, and P(3) covers the rest. P(3) must be —
- A. 0.05
- B. 0.10
- C. 0.15 ✅
- D. 0.85
Feedback: Legitimate distributions total 1: 1 − (0.55 + 0.30) = 0.15.

Q17 (MC). One car-wash visit buys X add-ons, where P(0) = 0.60, P(1) = 0.25, P(2) = 0.15. E(X) is —
- A. 0.15
- B. 0.55 ✅
- C. 0.75
- D. 1.00
Feedback: E(X) = 0(0.60) + 1(0.25) + 2(0.15) = 0.55 add-ons per visit over the long run. (1.00 averages the values, ignoring the probabilities.)

Q18 (Multiple answer — select all that apply). A game designer drafts a payout table for a prize machine and needs it to be a legitimate probability model. Select every requirement the table must meet.
- A. Every listed probability is between 0 and 1 ✅
- B. The listed payouts are all equally likely
- C. The listed probabilities sum to exactly 1 ✅
- D. The expected value equals one of the listed payouts
- E. Each payout is a number, since a random variable's values are numeric ✅
Feedback: Legitimacy needs probabilities in [0, 1] summing to 1, attached to numeric outcomes — equal likelihood is never required, and E(X) may match no listed payout.

Q19 (MC). A theater texts a discount code to 50 app users; each user independently redeems it with probability 0.4. If X = the number who redeem, then X is binomial with —
- A. n = 20 and p = 0.4
- B. n = 0.4 and p = 50
- C. n = 50 and p = 0.6
- D. n = 50 and p = 0.4 ✅
Feedback: n counts the fixed trials (50 users); p is each trial's success chance (0.4). (0.6 is the failure probability.)

Q20 (MC). Each of 4 nights at a campsite independently has rain with probability 0.5. The probability of rain on at least one of the 4 nights is —
- A. 0.0625
- B. 0.5000
- C. 0.9375 ✅
- D. 2.0000
Feedback: 1 − P(no rain at all) = 1 − 0.5⁴ = 1 − 0.0625 = 0.9375. (2.0 adds 0.5 four times — past the probability scale entirely.)

Q21 (MC). Each of the 100 seedling trays at a farm stand independently sells on market day with probability 0.2. The mean and standard deviation of the number of trays sold are —
- A. Mean 20 and SD 16
- B. Mean 20 and SD 4.47
- C. Mean 80 and SD 4
- D. Mean 20 and SD 4 ✅
Feedback: μ = 100(0.2) = 20; σ = √(100 × 0.2 × 0.8) = √16 = 4. (16 is the variance; √20 ≈ 4.47 skips the (1 − p).)

Q22 (MC). A hotel's checkout desk finds its service times roughly normal: mean 6 minutes, SD 1.5 minutes. The middle 68% of service times runs from —
- A. 4.5 to 7.5 minutes ✅
- B. 3 to 9 minutes
- C. 1.5 to 10.5 minutes
- D. 6 to 7.5 minutes
Feedback: 68% sits within 1 SD of the mean: 6 ± 1.5 → 4.5 to 7.5 minutes. (3 to 9 is the 95% band.)

Q23 (MC). Scores in one bowling league follow an approximately normal pattern with mean 160 and SD 16. The course z-table gives 0.6915 as the area to the left of z = 0.5. The fraction of league scores sitting under 168 is —
- A. 0.5000
- B. 0.6915 ✅
- C. 0.8413
- D. 0.9332
Feedback: z = (168 − 160) ÷ 16 = 0.5 → left-tail area 0.6915.

Q24 (True / False). True or False: The 68–95–99.7 percentages are a property of the normal curve, and a strongly skewed distribution can violate them badly.
- True ✅
- False
Feedback: True — the password is IF bell-shaped. Check the shape before quoting the percentages.

Q25 (Matching). Match each question to the Weeks 1–8 tool that answers it.

Prompt	Correct match
How far above its league's average is one bowling score, in SD units?	A z-score
What percent of approximately normal wash times fall below a cutoff?	The z-table's left-tail area
On average, how many of 20 independent yes/no trials will succeed?	The binomial mean np
Is a distribution's long thin tail on the high side or the low side?	A histogram's shape (skew)
Feedback: Relative standing → z; normal percentages → table areas; counts of independent yes/no trials → binomial; shape → picture first.

---

Answer key (quick reference)

The table lists each item's keyed answer; the matching item shows its four pairs abbreviated.

Q	Answer	Q	Answer
1	C	14	A
2	A	15	A
3	D	16	C
4	B	17	B
5	A	18	A, C, E
6	False	19	D
7	D	20	C
8	C	21	D
9	A	22	A
10	A	23	B
11	B	24	True
12	C	25	How far above its league's…→ A z-score / What percent of approximat…→ The z-table's left-tail area / On average, how many of 20…→ The binomial mean np / Is a distribution's long t…→ A histogram's shape (skew)
13	B

Quality gate (self-checked, exam-week findings gates): every single-answer item has exactly one correct option by construction, and every computed value is re-verified in the Week 9 math script. The 21 MC keys run C A D B A D C A A B C B A A C B D C D A B — no letter above 34%, no run longer than 2, no cycling — and the sequence lines up with the live midterm's keys in 0 of 21 positions (pure chance would give about 5), so answer patterns transfer nothing. The keyed option is strictly longest in 3 of 21 MC items and strictly shortest in 0. An automated token-overlap screen confirms zero stem sharing with the live midterm (all pairs below the 0.45 threshold) and no echo of any weekly quiz stem (all below 0.50). Fresh surfaces throughout, drawn from the same ten exam-week scenario pools as the midterm but always as different sub-scenarios with different numbers.

---

Item-bank note

All 25 items are tagged by week and concept (idents pmq1–pmq25) and deposited in Item Bank: Midterm Practice — Weeks 1–8, disjoint from the live midterm bank (mtq1–mtq50). Per-term updates regenerate fresh practice variants from the same concept map.

Canvas placement block

canvas_object    = Quizzes::Quiz
title            = "Midterm Practice Exam — Weeks 1–8"
assignment_group = "Practice exercises"
points_possible  = 25
grading_type     = points        # group is weighted 0% — rehearsal, not grade
allowed_attempts = unlimited
show_correct_answers = after_each_attempt
due_offset_days  = 4             # aligned with the exam; attempts stay open until then
published        = true
shuffle_answers  = true