Here is the truth nobody tells you on exam morning: you already know the statistics. Twenty-nine lessons of distributions, conditions, and p-values are sitting in your head. What separates a 3 from a 5 is rarely "more content" — it's game management. It's knowing that an FRQ point is a physical thing you either grab or leave on the table. It's not burning four minutes on one stubborn multiple-choice question when twelve easy ones are still waiting. It's writing "we have convincing evidence that the true mean fill is less than 16 ounces" instead of just "reject H₀," because the second version earns you nothing.
The AP Statistics exam is not a hostile puzzle. It is a point-collection game with published rules, and today you learn the rules. We will lay out the exact format, do the pacing arithmetic, walk through how MC and FRQ points are actually awarded, build a procedure-selection map so you never freeze on "which test is this," catalog the ten errors that quietly cost the most points, and finish with a mixed multiple-choice warm-up spanning all five units. You know the statistics. Now master the game.
The May 2027 exam is the first administration of the revised format. Memorize this table — knowing the structure removes exam-day anxiety and lets you pace yourself instinctively.
| Section I | Section II | |
|---|---|---|
| Type | Multiple choice | Free response |
| Questions | 42 questions | 4 questions |
| Time | 90 minutes | 90 minutes |
| Weight | 50% of score | 50% of score |
| Answer choices | 4 per question (A–D) | n/a |
| Scoring | 1 point each, no penalty for guessing | 10 points each, point-based |
| Calculator | Allowed on ALL questions | Allowed on ALL questions |
| Coverage | All 5 units | Roles below |
The four FRQs are not random — each targets specific Statistical Practices, so you can predict the shape of each before you read it.
Section I: 90 minutes ÷ 42 questions = ~2 min 9 sec per MC. That is generous. Many questions take 30–45 seconds; bank that saved time for the 5–6 hard ones.
Section II: 90 minutes ÷ 4 FRQs = ~22–23 minutes per FRQ. Do not spend 40 minutes loving FRQ 3 and leave FRQ 4 blank — a blank question is a guaranteed zero, and the easy first parts of FRQ 4 are usually worth more than the last grind-it-out point of FRQ 3.
A practical Section II plan: skim all four FRQs first (2 minutes), start with the one you find easiest to build momentum and points, and keep a hard eye on the clock at the 22-minute marks.
A formula sheet is provided on exam day. It gives you descriptive-statistics formulas, probability formulas, the standard-error and test-statistic templates, and sampling-distribution formulas. What it will not do for you:
A graphing calculator with statistical capability (TI-84 family) is required and allowed on every question in both sections. Use it to do arithmetic fast and to run the inference engines (1-PropZTest, T-Test, χ²-Test, etc.). But remember: the calculator gives the number; you give the meaning. A bare calculator answer with no parameter, no conditions, and no context is worth a fraction of the points.
Forty-two questions, four choices, one point each, no penalty for wrong answers. Three consequences follow immediately:
Process of elimination. Most stats MC distractors are engineered mistakes: the right number with the wrong sign, a standard error using p̂ when it should use p₀, a "fail to reject" flipped to "reject." Cross out the choices you can prove wrong. If two of four are gone, your guess is 50/50.
Plug in and estimate. With a calculator on every question, you can often test choices directly. For a "which is the test statistic" question, just compute it. For a probability, run normalcdf or binompdf. When numbers look ugly, estimate: a z-score near 2 puts a tail probability near 0.025; a correlation that "looks strong and positive" is near +0.8, not +0.3.
Reading data displays. A large share of MC is reading boxplots, histograms, two-way tables, and regression printouts. Practice pulling the median and IQR off a boxplot, the shape off a histogram, and the slope, intercept, r², and s off a computer regression output. These are fast points if you've drilled them — recall that r = √(r²) with the sign of the slope.
Use the calculator efficiently. Know the one number each engine reports: 1-PropZTest and T-Test give you the test statistic and the p-value; TInterval and 1-PropZInt give the interval endpoints; χ²-Test gives χ², df, and p. Don't re-derive by hand what the calculator hands you in two keystrokes.
Time triage. Do a first pass answering everything you can in under ~60 seconds. Flag and skip anything that stalls you. Second pass: spend the banked time on flagged questions. If you're still stuck at the end, eliminate and guess — never blank.
Under the new format each FRQ is worth 10 points, scored point-by-point against a rubric — not holistically. A point is awarded for a specific identifiable action: stating the correct parameter, naming the procedure, checking a condition, computing a statistic, drawing the right conclusion, linking that conclusion to the p-value. The grader is essentially running down a checklist with your paper. Your job is to make every checklist item easy to find and tick. That means: label your steps, write in complete sentences for interpretations, and show the substitution before the final number.
The single biggest FRQ lever is communication. Two students can reach the same p-value; the one who writes a complete, contextual conclusion outscores the one who writes "reject H₀" by several points across the exam.
Any confidence interval or significance test follows the same five-beat march. Write the letters in your margin and you will not forget a point.
These are the lines that separate a 5 from a 3. On every inference FRQ:
FRQ 4 is multi-part and crosses content areas. Strategy:
Scenario. A coffee chain advertises that its large iced coffee contains 16 ounces. A consumer-protection investigator suspects the machines are off-target. She takes a random sample of 20 large iced coffees from one store, measures each, and finds a sample mean of x̄ = 15.78 oz with sample standard deviation s = 0.42 oz. A dotplot of the 20 values is roughly symmetric with no outliers. Is there convincing evidence at α = 0.05 that the true mean fill differs from 16 oz?
Model response (PANIC):
P — Parameter. Let μ = the true mean fill volume (in ounces) of all large iced coffees produced by this store's machine.
Hypotheses. H₀: μ = 16 versus Hₐ: μ ≠ 16 (two-sided — "differs from").
A — Assumptions / conditions.
N — Name the procedure. A one-sample t-test for a mean.
I — Test computation.
SE = s / √n = 0.42 / √20 = 0.0939
t = (x̄ − μ₀) / SE = (15.78 − 16) / 0.0939 = −2.343
df = n − 1 = 19
p-value = 2 · P(t₁₉ < −2.343) = 0.030TI-84: STAT → TESTS → T-Test, Stats, μ₀=16, x̄=15.78, Sx=0.42, n=20, μ:≠μ₀ → t = −2.343, p = 0.030.
C — Conclusion in context. Because p = 0.030 < α = 0.05, we reject H₀. There is convincing evidence that the true mean fill volume of this store's large iced coffees differs from (is below) 16 ounces.
10-point rubric:
| Pts | Awarded for |
|---|---|
| 1 | Parameter μ defined in context (true mean fill, this machine, oz) |
| 1 | Correct hypotheses H₀: μ = 16, Hₐ: μ ≠ 16 (two-sided) |
| 1 | Random condition checked |
| 1 | 10%/independence condition checked |
| 1 | Normal condition addressed via the dotplot (symmetric, no outliers) |
| 1 | Procedure correctly named (one-sample t-test) |
| 1 | Correct test statistic t = −2.343 (with df = 19) |
| 1 | Correct p-value ≈ 0.030 |
| 1 | Correct decision linked to α: p < 0.05 → reject H₀ |
| 1 | Conclusion stated in context (mean fill differs from 16 oz) |
The most common FRQ-3 freeze is "which procedure is this?" This table is your decision guide. Read the scenario, match the signals, pick the row.
| Scenario signal | Procedure | Key conditions |
|---|---|---|
| One categorical variable, one sample, question about a single proportion | One-proportion z-interval / z-test | Random; 10%; Large Counts (use p₀ for the test, p̂ for the interval) |
| Two independent groups, compare two proportions | Two-proportion z-interval / z-test | Random; 10% each; Large Counts in both groups (test uses pooled p̂) |
| Several separate samples, one categorical response, compare distributions | χ² test for homogeneity | Random; 10%; all expected counts ≥ 5 |
| One sample, two categorical variables on the same people, test association | χ² test for independence | Random; 10%; all expected counts ≥ 5 |
| One quantitative variable, one sample, question about a single mean | One-sample t-interval / t-test (df = n−1) | Random; 10%; Normal/large (n ≥ 30 or roughly symmetric, no outliers) |
| Two independent groups, compare two means | Two-sample t-interval / t-test | Random; 10% each; both groups Normal/large |
| Paired measurements (before/after, two on same subject) — analyze the differences | Matched-pairs t (one-sample t on the diffs, df = n−1) | Random assignment/pairing; 10%; differences Normal/large |
| Two quantitative variables, describe the linear relationship | Regression: scatterplot, r, LSRL, r², residuals (description only) | Linear pattern; no inference for slope on the new exam |
The deciding questions: (1) Is the response categorical (proportions / χ²) or quantitative (means / regression)? (2) One sample or two? (3) Are two quantitative samples independent or paired? Answer those three and the row is forced.
Ranked by how many points they quietly cost across a full exam. Each comes with the fix.
p̂ instead of p₀. Fix: a one-proportion test uses √(p₀(1−p₀)/n); the interval uses √(p̂(1−p̂)/n). Two-proportion test uses the pooled p̂.Fourteen four-choice questions spanning all five units, mixed difficulty. Calculator allowed (as on the real exam). Answer key with full reasoning follows.
1. (Unit 1 — Normal) Adult female heights are approximately Normal with mean 64 in and standard deviation 2.7 in. What proportion of women are taller than 68 inches?
2. (Unit 1 — Boxplots) A data set has Q₁ = 18 and Q₃ = 30. Using the 1.5 × IQR rule, a value is flagged as a high outlier if it exceeds:
3. (Unit 1 — Design) Researchers measure each subject's blood pressure before and after taking a drug, then analyze the change for each subject. This is best described as:
4. (Unit 1 — Spread) Which statement about the standard deviation is correct?
5. (Unit 2 — Binomial) A multiple-choice quiz has 10 questions, each with probability 0.3 of being answered correctly by guessing. What is the probability of getting exactly 3 correct?
6. (Unit 2 — Expected value) A game pays \$0 with probability 0.5, \$5 with probability 0.3, and \$10 with probability 0.2. The expected payoff is:
7. (Unit 2 — Sampling distribution of x̄) A population has μ = 500 and σ = 100. For samples of size n = 25, the standard deviation of the sampling distribution of x̄ is:
8. (Unit 2 — Sampling distribution of p̂) A population proportion is p = 0.4. For an SRS of size 50, the standard deviation of p̂ is approximately:
9. (Unit 3 — CI interpretation) A 95% confidence interval for a population proportion is (0.52, 0.60). Which interpretation is correct?
10. (Unit 3 — Procedure choice) A researcher takes one random sample of 400 adults and records both their political party (3 categories) and whether they support a policy (yes/no), then asks whether party and support are related. The appropriate procedure is:
11. (Unit 3 — Chi-square df) A χ² test is run on a two-way table with 3 rows and 4 columns. The degrees of freedom are:
12. (Unit 4 — One-sample t interval) From a random sample of n = 16 with x̄ = 50 and s = 8, a 95% confidence interval for μ uses t* = 2.131 (df = 15). The interval is approximately:
13. (Unit 4 — Paired vs. two-sample) Twelve volunteers each try two keyboard layouts and have their typing speed measured on both. To compare the layouts, the correct procedure is:
14. (Unit 5 — Correlation) A least-squares regression of exam score on study hours has a positive slope and r² = 0.64. The correlation coefficient r is:
15. (Unit 5 — Prediction) A least-squares line is ŷ = 5.2 + 8.1x, where x is study hours and ŷ is predicted exam score. The predicted score for a student who studies 4 hours is:
1. (A) 0.069. z = (68 − 64)/2.7 = 1.481; P(Z > 1.481) = 1 − 0.9308 = 0.069 (TI-84: normalcdf(68, 1E99, 64, 2.7)). (B) 0.093 is a miscomputed z. (C) 0.481 is the area between mean and z mis-read. (D) 0.931 is the left tail — the proportion shorter than 68.
2. (C) 48. IQR = 30 − 18 = 12; upper fence = Q₃ + 1.5·IQR = 30 + 18 = 48. (A) 36 = Q₃ + 0.5·IQR. (B) 42 = Q₃ + IQR (forgot the 1.5). (D) 60 = 2·Q₃.
3. (B) Matched-pairs design. Each subject provides two linked measurements (before/after), analyzed as one set of differences. (A) is for two separate groups. (C) is a sampling method, not an experimental design. (D) ignores that a treatment (the drug) is imposed.
4. (C) Zero only when all observations are identical. SD measures spread; no spread ⇒ SD = 0. (A) is false — SD is not resistant; outliers inflate it. (B) is false — SD is never negative (it's a root of a sum of squares). (D) is false — multiplying every value by 3 multiplies the SD by 3 (it's adding a constant that leaves SD unchanged).
5. (B) 0.267. Binomial: C(10,3)(0.3)³(0.7)⁷ = 120 · 0.027 · 0.0823543 = 0.267 (TI-84: binompdf(10, 0.3, 3)). (A) 0.200, (C) 0.300, (D) 0.650 are plausible-looking values with no correct derivation; (C) is the tempting "p itself" trap.
6. (A) \$3.50. E(X) = 0(0.5) + 5(0.3) + 10(0.2) = 0 + 1.5 + 2.0 = 3.5. (B) \$5 and (C) \$6 ignore the weighting; (D) \$7.50 averages only the nonzero payoffs.
7. (B) 20. σ_x̄ = σ/√n = 100/√25 = 100/5 = 20. (A) 4 divides by n instead of √n incorrectly (100/25). (C) 100 forgets to divide. (D) 500 confuses with the mean.
8. (B) 0.069. σ_p̂ = √(p(1−p)/n) = √(0.4·0.6/50) = √0.0048 = 0.0693. (A) 0.0048 is the variance (forgot the square root). (C) 0.245 = √(0.4·0.6) without dividing by n. (D) 0.490 ≈ √(0.4·0.6) doubled / unrelated.
9. (C). Confidence is a property of the long-run method. (A) confuses the interval with a range of data. (B) is the classic error — a single computed interval already does or does not contain the fixed p; there's no probability left. (D) describes a sampling distribution of p̂, not a confidence statement.
10. (B) χ² test for independence. One sample, two categorical variables (party and support) measured on the same people, testing whether they're related ⇒ independence. (A) needs a single yes/no variable across two groups. (C) homogeneity needs several separate samples. (D) is for a single proportion.
11. (B) 6. df = (r − 1)(c − 1) = (3 − 1)(4 − 1) = 2 · 3 = 6. (A) 5 = r + c − 2 (wrong rule). (C) 7 = r + c. (D) 12 = r · c (forgot to subtract).
12. (B) (45.7, 54.3). Margin = t·s/√n = 2.131·8/√16 = 2.131·2 = 4.26; 50 ± 4.26 = (45.74, 54.26). (A) rounds the margin to 4. (C) uses s/n instead of s/√n (margin 2). (D) uses t·s = 2.131·8 ≈ 17 incorrectly / forgets √n entirely (margin ~7.4).
13. (B) Matched-pairs t-test on the differences. Each volunteer is measured on both layouts — the two measurements are linked, so analyze the within-person differences. (A) wrongly treats them as independent groups. (C) and (D) are categorical procedures; typing speed is quantitative.
14. (D) 0.80. r = ±√r² = ±√0.64 = ±0.80; the slope is positive, so r = +0.80. (A) −0.80 has the wrong sign. (B) 0.41 ≈ 0.64² (squared instead of square-rooted). (C) 0.64 confuses r with r².
15. (C) 37.6. ŷ = 5.2 + 8.1(4) = 5.2 + 32.4 = 37.6. (A) 13.3 ≈ 5.2 + 8.1 (used x = 1). (B) 32.4 forgets the intercept. (D) 45.8 over-adds.
StatsIQ · Lesson 30 of 30 — capstone · Aligned to the 2026–27 AP Statistics framework. Not affiliated with the College Board. AP is a registered trademark of the College Board. Content pending statistical-accuracy review (Isaac).