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Exam Prep

AP Statistics: study sheet

9 units, with a key formula and what each covers, from this hub's syllabus notes. Not yet checked by a teacher: check it against your own notes.

The exam

Section I: 40 multiple-choice questions in 1 hr 30 min, 50% of the score. Section II: 6 free-response questions in 1 hr 30 min, 50% (Part A: 5 questions; Part B: 1 investigative task). A graphing calculator is allowed throughout, and a formula sheet and tables are given. Source: College Board, AP Statistics Course and Exam Description.

Scored 1–5. Unit weightings are the College Board's published ranges for the multiple-choice section.

  1. 1. Unit 1: Exploring One-Variable Data

    15–23% of exam score

    z=x−μσz = \frac{x - \mu}{\sigma}

    • Graphs of one-variable data

    • Centre, spread and outliers

    • Comparing distributions

    • Normal distributions and z-scores

  2. 2. Unit 2: Exploring Two-Variable Data

    5–7% of exam score

    y^=a+bx,b=r sysx\hat{y} = a + bx, \quad b = r\,\frac{s_y}{s_x}

    • Two-way tables

    • Scatterplots and correlation

    • Least-squares regression

    • Residuals and departures from linearity

  3. 3. Unit 3: Collecting Data

    12–15% of exam score

    Random assignment⇒cause and effect; random sampling⇒generalisation\text{Random assignment} \Rightarrow \text{cause and effect; random sampling} \Rightarrow \text{generalisation}

    • Sampling methods

    • Sources of bias

    • Observational studies and experiments

    • Experimental design: blocking and control

  4. 4. Unit 4: Probability, Random Variables, and Probability Distributions

    10–20% of exam score

    P(X=k)=(nk)pk(1−p)n−kP(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}

    • Probability rules and simulation

    • Conditional probability and independence

    • Mean and standard deviation of random variables

    • Binomial and geometric distributions

  5. 5. Unit 5: Sampling Distributions

    7–12% of exam score

    σxˉ=σn\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}

    • Sampling distribution of a proportion

    • Sampling distribution of a mean

    • Central limit theorem

    • Biased and unbiased estimators

  6. 6. Unit 6: Inference for Categorical Data: Proportions

    12–15% of exam score

    p^±z∗p^(1−p^)n\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}

    • Confidence intervals for proportions

    • Significance tests for proportions

    • Type I and Type II errors

    • Two-sample proportions

  7. 7. Unit 7: Inference for Quantitative Data: Means

    10–18% of exam score

    t=xˉ−μ0s/nt = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}

    • t-distributions

    • Intervals and tests for one mean

    • Paired data

    • Two-sample means

  8. 8. Unit 8: Inference for Categorical Data: Chi-Square

    2–5% of exam score

    χ2=∑(O−E)2E\chi^2 = \sum \frac{(O - E)^2}{E}

    • Goodness of fit

    • Homogeneity

    • Independence

    • Expected counts and conditions

  9. 9. Unit 9: Inference for Quantitative Data: Slopes

    2–5% of exam score

    t=b−β0SEb,df=n−2t = \frac{b - \beta_0}{SE_b}, \quad df = n - 2

    • Conditions for regression inference

    • Confidence interval for a slope

    • Test for a slope

    • Reading computer regression output