Twenty-four exam-style questions. Tap a question to reveal the worked answer.
⭐ How to use this page
Same mix as the final: data types, describing data, correlation, probability, normal, CLT, confidence intervals, hypothesis tests. Work each one on paper or in Desmos before you tap the answer. Numbers are rounded to the same places the key usually uses; a tiny difference in the last decimal is Desmos vs. table rounding, not a mistake.
❓ 2. “Of the 300 patients surveyed, 22% were satisfied.” Identify the population, the sample, and whether 22% is a parameter or a statistic.
Population: all of the hospital’s patients. Sample: the 300 surveyed. 22% is a statistic (from the sample) used to estimate the parameter p.
❓ 3. Patients who chose to join a walking program had lower HbA1c a year later than those who did not. Can we conclude walking lowered HbA1c?
No. This is an observational study: patients self-selected. A lurking variable (motivation, diet, baseline health) could explain both. Only a randomized experiment supports cause.
📈 Describing data
❓ 4. Resting heart rates for 10 patients: 64, 72, 68, 80, 76, 70, 66, 88, 74, 72. Find the mean, median and sample SD.
Sort: 64, 66, 68, 70, 72, 72, 74, 76, 80, 88. Mean = 730/10 = 73. Median = (72 + 72)/2 = 72. s = 7.07 bpm (Desmos: stdev(L)).
❓ 5. In Q4, is the 88 an outlier by the 1.5 × IQR rule? (Use Q1 = 68, Q3 = 76.)
IQR = 8. Upper fence = 76 + 1.5(8) = 88. The 88 sits exactly on the fence, so it is not beyond it — not an outlier by this rule. (Anything above 88 would be.)
❓ 6. A histogram of hospital charges has a long right tail. Which measure of center should you report, and why?
Median. The mean is pulled up by the few enormous bills; the median describes the typical patient.
❓ 7. Two units record daily census. Unit A: mean 24, SD 2. Unit B: mean 24, SD 7. What does the SD difference mean in practice?
Both average 24 patients, but Unit B swings much more day to day (roughly 17 to 31 on most days vs 22 to 26 on A). Staffing B is harder to predict.
📉 Correlation and regression
❓ 8. Days after surgery (x) vs pain score (y): (1, 3.1), (2, 2.6), (3, 2.2), (4, 1.5), (5, 1.1), (6, 0.7). Describe the relationship and give r (Desmos).
Strong negative linear: pain drops as days pass. r = -0.997. Line: ŷ = -0.491x + 3.587.
❓ 9. Using the line from Q8, predict pain on day 4 and interpret the slope. Would you predict pain on day 30?
Day 4: -0.491(4) + 3.587 = 1.62. Slope -0.49: pain falls about 0.49 points per day. Day 30 is extrapolation (data stop at day 6, and the line would go negative) — do not predict.
🎲 Probability
❓ 10. On a unit 45% of patients are on anticoagulants (A), 30% are on insulin (B), and 12% are on both. Find P(A or B) and decide whether A and B are independent.
P(A or B) = 0.45 + 0.30 − 0.12 = 0.63. Independent would need P(A and B) = 0.45 × 0.30 = 0.135; actual is 0.12, so not independent.
❓ 11. A rapid flu test has sensitivity 80% and specificity 96%. In a clinic where 25% of symptomatic patients have flu, what is the PPV?
Per 1,000 patients: 250 flu → 200 test +; 750 no flu → 4% = 30 test +. PPV = 200/230 = 0.87. P(flu | positive) ≠ P(positive | flu).
❓ 12. 15% of patients react to a contrast dye. Of 6 patients scanned today, find P(exactly 2 react) and P(at least 1 reacts).
❓ 14. Adult LDL cholesterol on a clinic panel: μ = 135 mg/dL, σ = 12. What proportion of adults have LDL below 120? Above 150?
Below 120: z = −1.25 → 0.1056. Above 150: z = 1.25 → 0.1056. (Symmetric, so they match.) Desmos: normaldist(135,12).cdf(−infty,120).
❓ 15. Same LDL distribution. What LDL value marks the 95th percentile?
z = 1.645 → x = 135 + 1.645(12) = 154.7 mg/dL. Desmos: normaldist(135,12).inversecdf(0.95).
❓ 16. Same LDL distribution. For a random sample of 16 adults, what is P(the sample mean is above 140)?
SE = 12/√16 = 3. z = (140 − 135)/3 = 1.67 → 0.0478. Desmos: normaldist(135, 12/sqrt(16)).cdf(140, infty).
❓ 17. Length of stay is strongly skewed right with μ = 4.2 and σ = 2.1 days. Why can you still use the normal curve for the mean of 50 stays, and what is its SD?
The Central Limit Theorem: for n ≥ 30 the sampling distribution of x̄ is approximately normal regardless of the population’s shape. SD of x̄ = 2.1/√50 = 0.297 days.
⚖️ Confidence intervals and hypothesis tests
❓ 18. 50 post-op patients: mean pain 4.6, s = 1.8. Build a 95% CI for the mean pain score and interpret it.
df = 49, t* = 2.010. E = 2.010 · 1.8/√50 = 0.517. CI: (4.08, 5.12). “We are 95% confident the mean pain score of all such post-op patients is between 4.08 and 5.12.”
❓ 19. 105 of 300 surveyed nurses plan to leave bedside nursing within 2 years. Give a 90% CI for the proportion.
p̂ = 0.35. SE = √(0.35 · 0.65/300) = 0.0275. E = 1.645 × 0.0275 = 0.045. CI: (0.305, 0.395), about 30% to 40%.
❓ 20. You want to estimate mean HbA1c within ±0.25 at 95% confidence; σ ≈ 0.8. How many patients?
n = (1.96 · 0.8/0.25)² = 39.34 → round up: 40.
❓ 21. The target mean HbA1c on a diabetes program is 7.5. 30 enrolled patients average 7.9 with s = 1.2. At α = 0.05, is the mean higher than target?
H₀: μ = 7.5, Hₐ: μ > 7.5. t = (7.9 − 7.5)/(1.2/√30) = 1.83, df = 29. p = 0.0391 (tdist(29).cdf(1.83, infty)). 0.0391 < 0.05 → reject H₀: evidence the program mean is above 7.5.
❓ 22. A vendor claims its catheter has a 15% infection rate. In 400 uses at your hospital, 48 infections occurred. Is the rate lower than claimed? α = 0.05.
p̂ = 0.12. H₀: p = 0.15, Hₐ: p < 0.15. SE = √(0.15 · 0.85/400) = 0.01785. z = (0.12 − 0.15)/0.01785 = -1.68. p = P(Z < -1.68) = 0.0464 < 0.05 → reject H₀: your rate is significantly lower.
❓ 23. In Q22, describe a Type I and a Type II error in words.
Type I: concluding your rate is lower than 15% when it really is not (a false alarm). Type II: your rate really is lower, but the test failed to show it.
❓ 24. A 95% CI for the mean difference in wound-healing days (new dressing minus old) is (−3.1, −0.4). What does a two-tailed test at α = 0.05 conclude about H₀: difference = 0?
The interval does not contain 0, so the test rejects H₀: the new dressing changes healing time (it heals faster, by 0.4 to 3.1 days).
MAT 300 · built from your own course files (the statistics study guide, the Desmos guide, the formula sheet and the final-exam study questions) with nursing examples. Not a substitute for the textbook — check any number against your own notes before an exam.