College Board Exam Prep

AP Statistics

20 Essential Concept Questions · All Major Units

📊 20 Questions ⏱ 40 Min Suggested 🎯 Exam-Style MCQ 📐 All Units Covered
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Unit 1 · Exploring One-Variable Data
  • Shape: symmetric, skewed left/right, unimodal, bimodal
  • Center: mean (x̄), median — mean is sensitive to outliers, median is resistant
  • Spread: range, IQR = Q3 − Q1, standard deviation (s)
  • Outlier rule: value < Q1 − 1.5·IQR or > Q3 + 1.5·IQR
  • z-score: z = (x − μ) / σ — measures standard deviations from mean
IQR = Q3 − Q1  |  z = (x − μ)/σ  |  Outlier: x < Q1−1.5·IQR or x > Q3+1.5·IQR
Unit 2 · Exploring Two-Variable Data
  • Scatterplot: direction, form (linear/non-linear), strength, outliers
  • Correlation r: −1 ≤ r ≤ 1; r near ±1 = strong linear; r = 0 = no linear association
  • LSRL: ŷ = a + bx where b = r·(sy/sx), a = ȳ − b·x̄
  • r² (coefficient of determination): % variation in y explained by LSRL
  • Residual = observed y − predicted ŷ; residual plot should show no pattern
ŷ = a + bx  |  b = r(sᵧ/sₓ)  |  a = ȳ − bx̄  |  residual = y − ŷ
Unit 3 · Collecting Data
  • SRS: every sample of size n has equal chance of selection
  • Stratified: divide into strata, SRS from each stratum
  • Cluster: divide into clusters, randomly select entire clusters
  • Systematic: select every kth individual from list
  • Experiment vs. Observational Study: only experiments can establish causation
  • Blocking: groups of experimental units that are similar; reduces variability
  • Confounding variable: variable associated with both explanatory and response
Unit 4 · Probability, Random Variables & Distributions
  • P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
  • Independence: P(A ∩ B) = P(A)·P(B)    P(A|B) = P(A)
  • E(X) = μ = Σ[x·P(x)]    Var(X) = Σ[(x−μ)²·P(x)]
  • Binomial: n trials, each success p, X = # successes; μ=np, σ=√(np(1−p))
  • Geometric: # trials until first success; μ = 1/p
  • Normal distribution: 68-95-99.7 rule
P(X=k) = C(n,k)·pᵏ·(1−p)ⁿ⁻ᵏ  |  μ=np  |  σ=√(np(1−p))
Unit 5 · Sampling Distributions
  • Sampling dist. of x̄: mean = μ, SD = σ/√n (standard error)
  • CLT: for large n (≥30), x̄ is approx. Normal regardless of population shape
  • Sampling dist. of p̂: mean = p, SD = √(p(1−p)/n)
  • Normal approximation for p̂: np ≥ 10 and n(1−p) ≥ 10
  • Bias: systematic error (sampling method flaw)
  • Variability: spread of sampling distribution; decreases as n increases
SE(x̄) = σ/√n  |  SE(p̂) = √(p(1−p)/n)
Unit 6-7 · Inference: Proportions & Means
  • CI = statistic ± (critical value)(standard error)
  • Margin of error = z*·SE; wider CI → less precision; larger n → narrower CI
  • H₀ (null hypothesis) vs. Hₐ (alternative hypothesis)
  • p-value: probability of observed result (or more extreme) if H₀ is true
  • Reject H₀ if p-value < α (significance level, typically 0.05)
  • Type I error: reject true H₀ (α = probability of Type I error)
  • Type II error: fail to reject false H₀ (β = probability); Power = 1 − β
  • t-distribution: use when σ unknown; df = n − 1
  • Two-sample t-test: compares means of two independent groups
  • Paired t-test: differences within matched pairs
z* for 95% CI ≈ 1.96  |  t* depends on df  |  df = n−1
Unit 8-9 · Chi-Square & Regression Inference
  • Chi-square GOF: tests if observed counts match expected distribution; df = k−1
  • Chi-square homogeneity: same distribution across populations; df=(r−1)(c−1)
  • Chi-square independence: association between two categorical variables
  • Expected count = (row total × column total) / grand total
  • Regression inference: t-test for slope β; H₀: β = 0 (no linear relationship)
  • Conditions: Linearity, Independence, Normal residuals, Equal variance (LINE)
χ² = Σ[(O−E)²/E]  |  Expected = (row total × col total) / n

AP Statistics Practice Exam

20 Multiple Choice Questions · All Units · Name: _________________ Date: ___________

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Unit 1 · One-Variable Data Medium

A dataset has the following five-number summary: Min = 12, Q1 = 25, Median = 40, Q3 = 55, Max = 90. Which of the following values would be classified as an outlier according to the 1.5 × IQR rule?

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Unit 1 · One-Variable Data Medium

A distribution of test scores is strongly skewed to the right. Which of the following correctly compares the mean and median?

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Unit 2 · Two-Variable Data Medium

A least-squares regression line for predicting weight (lbs) from height (inches) is \(\hat{y} = -120 + 4.5x\). The value 4.5 in this equation means:

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Unit 2 · Two-Variable Data Hard

In a study, the correlation between hours studied and exam score is r = 0.85. The coefficient of determination is 0.7225. Which of the following is the correct interpretation?

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Unit 3 · Collecting Data Medium

A researcher wants to study the effect of a new medication on blood pressure. Patients are randomly assigned to either receive the medication or a placebo. Neither the patients nor the doctors measuring blood pressure know which treatment was given. This design is best described as:

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Unit 3 · Collecting Data Hard

A school district divides its 1,200 students into 4 grade levels (9th–12th), then randomly selects 50 students from each grade. What type of sampling method is being used, and what is a key advantage of this method?

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Unit 4 · Probability Medium

Events A and B are independent with P(A) = 0.4 and P(B) = 0.3. What is P(A ∪ B)?

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Unit 4 · Binomial Distribution Hard

A fair coin is flipped 10 times. Let X = number of heads. What is the standard deviation of X?

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Unit 4 · Normal Distribution Medium

SAT scores are approximately normally distributed with mean μ = 1060 and standard deviation σ = 195. Approximately what percentage of students score between 865 and 1255?

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Unit 5 · Sampling Distributions Medium

A population has mean μ = 80 and standard deviation σ = 20. A random sample of n = 100 is taken. What is the standard error of the sample mean?

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Unit 5 · CLT Hard

Which of the following statements about the Central Limit Theorem (CLT) is correct?

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Unit 6 · Confidence Intervals Medium

A 95% confidence interval for the mean daily screen time of teenagers is (5.2, 6.8) hours. Which of the following is the correct interpretation?

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Unit 6 · Hypothesis Testing Hard

A p-value of 0.03 is obtained from a significance test conducted at α = 0.05. Which of the following is the correct conclusion?

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Unit 6 · Type I & II Errors Hard

A pharmaceutical company tests whether a new drug is effective. H₀: the drug has no effect. A Type II error in this context would be:

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Unit 7 · t-Procedures Medium

A researcher takes a random sample of 15 students and measures their reaction times. Which procedure should be used to construct a confidence interval for the true mean reaction time, and why?

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Unit 7 · Two-Sample Inference Hard

A study compares the mean test scores of students taught by Method A (n₁ = 30, x̄₁ = 82, s₁ = 8) and Method B (n₂ = 35, x̄₂ = 78, s₂ = 10). A two-sample t-test yields p-value = 0.08. At α = 0.05, the conclusion is:

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Unit 8 · Chi-Square Tests Medium

A chi-square goodness-of-fit test is conducted to determine whether a six-sided die is fair. The test uses 60 rolls. What are the degrees of freedom and the expected count for each outcome?

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Unit 8 · Chi-Square Independence Hard

A chi-square test of independence is performed on a 3×4 contingency table with a grand total of 200 observations. What is the expected count for the cell in row 2, column 3 if the row 2 total is 80 and the column 3 total is 50?

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Unit 9 · Regression Inference Hard

In regression inference, the null hypothesis H₀: β = 0 is tested. If the p-value for the t-test on the slope is 0.002, which conclusion is correct at α = 0.05?

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Unit 6 · Margin of Error Hard

A pollster wants to estimate the proportion of voters who support a candidate. The current estimate is p̂ = 0.5. To reduce the margin of error by half while maintaining 95% confidence, the sample size must be:

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