AP Statistics 3-Day Cram Plan

You have three days until the AP Statistics exam. This is not the time to relearn boxplots — it's time to drill the inference procedures that account for nearly half the exam and lock in the FRQ "state-plan-do-conclude" framework the College Board grades on every single test.

This plan assumes ~4 focused hours per day. If you're short on time, shorten the practice sets, not the topic coverage.

Day 1: Sampling, Study Design, and Probability Foundations (4 hrs)

These topics show up in MCQs, the FRQ on study design (always present), and as setup for every inference question.

What to review (90 min)

• Sampling methods: SRS, stratified, cluster, systematic, convenience. Know the difference, and know why SRS is gold-standard.
• Bias: undercoverage, nonresponse, response bias, voluntary response. Be able to name the type on an FRQ.
• Experiments vs observational studies: confounding, lurking variables, blocking, matched pairs, blinding, placebo.
• Random variables: $E(X) = \sum x \cdot P(x)$, $\text{Var}(X) = \sum (x - \mu)^2 P(x)$. Combinations: $E(X \pm Y) = E(X) \pm E(Y)$ always; $\text{Var}(X \pm Y) = \text{Var}(X) + \text{Var}(Y)$ only if independent.
• Normal distribution: $z = \frac{x - \mu}{\sigma}$. Use normalcdf and invNorm on the calculator.

What to practice (2.5 hrs)

• 20 mixed MCQs covering Units 1, 3, 4 (no inference yet).
• 1 full FRQ on study design — read it carefully. The rubric demands you address randomness AND control.

💡 Highest leverage: The study design FRQ is worth ~9 points and uses the same vocabulary every year. If you can describe random assignment, control of confounding variables, and replication clearly, you bank 6-8 points easily.

Day 2: Sampling Distributions + Confidence Intervals (4 hrs)

Sampling distributions are the conceptual bridge to inference. CIs make up roughly 15-20% of the exam.

What to review (90 min)

• Sampling distribution of $\hat p$: mean $= p$, $\sigma_{\hat p} = \sqrt{\frac{p(1-p)}{n}}$. Conditions: random, 10% (independence), Large Counts ($np \geq 10$ AND $n(1-p) \geq 10$).
• Sampling distribution of $\bar x$: mean $= \mu$, $\sigma_{\bar x} = \frac{\sigma}{\sqrt{n}}$. Central Limit Theorem (CLT) — sample size $n \geq 30$ for non-normal populations.
• CI structure: $\text{statistic} \pm \text{(critical value)} \times \text{(standard error)}$.
• CI types: 1-prop $z$, 2-prop $z$, 1-sample $t$, 2-sample $t$, paired $t$, LinReg $t$.
• Interpretation: "We are 95% confident that the true [parameter in context] is between [lower] and [upper] [units]." Memorize this.
• Confidence level interpretation (different!): "If we repeated this sampling procedure many times, about 95% of the resulting intervals would capture the true [parameter]."

What to practice (2.5 hrs)

• 15 MCQs on sampling distributions and CIs.
• 1 full FRQ that requires building a CI: state procedure name, check all 3 conditions in context, give calculator output, interpret in context.

⚠️ Don't say "the probability is 95% that the true mean is in this interval." That earns ZERO points. The interval either does or does not contain the parameter. The 95% refers to the procedure, not this specific interval.

Day 3: Significance Tests, Chi-Square, and Mock FRQs (4 hrs)

Significance tests are ~30% of the exam.

What to review (90 min)

• 4-step framework: State (hypotheses + parameter), Plan (procedure name + conditions in context), Do (test statistic + p-value), Conclude (compare to $\alpha$, reject/fail to reject in context).
• Tests to know: 1-prop $z$-test, 2-prop $z$-test, 1-sample $t$-test, 2-sample $t$-test, paired $t$-test, $\chi^2$ goodness-of-fit, $\chi^2$ test for independence/homogeneity, LinReg $t$-test for slope.
• Hypotheses: $H_0$: parameter = value (no effect). $H_a$: parameter $\neq$, $<$, or $>$ value.
• Test statistic forms: $z = \frac{\hat p - p_0}{\sqrt{p_0(1-p_0)/n}}$ (1-prop), $t = \frac{\bar x - \mu_0}{s/\sqrt{n}}$ (1-sample $t$), $\chi^2 = \sum \frac{(O-E)^2}{E}$.
• p-value interpretation: "Assuming $H_0$ is true, the probability of getting a sample statistic as extreme as or more extreme than ours is $p$."
• Type I error: reject true $H_0$. Type II error: fail to reject false $H_0$. Power: $1 - P(\text{Type II})$.

What to practice (2.5 hrs — full timed set)

• 1 full FRQ on a $t$-test or $z$-test (use the 4-step framework — write the words "State", "Plan", "Do", "Conclude" if it helps).
• 1 full FRQ on $\chi^2$.
• 25 mixed MCQs (calculator + non-calculator), strictly timed.

The night before

Skim our last-minute review checklist. Sleep 8 hours.

Calculator must-knows

Practice these on YOUR specific calculator (TI-84, TI-Nspire, etc.) tonight:

1. 1-PropZInt, 1-PropZTest (and 2-Prop versions).
2. TInterval, T-Test (and 2-SampTTest).
3. χ²-Test (chi-square for two-way tables) and χ²GOF-Test.
4. LinRegTTest for inference on slope.
5. normalcdf(lower, upper, μ, σ) and invNorm(area, μ, σ).
6. Stat → Edit to enter data into L1, L2; then 1-Var Stats L1 to get summary statistics.

Common point-leaks

• Skipping the 3 conditions check (Random / Independent / Normal — which means Large Counts for proportions, sample size $\geq 30$ for means, OR a stated normal population).
• Saying "$p$-value is the probability $H_0$ is true." It is not. $p$-value is conditional on $H_0$ being true.
• Forgetting "in context" — "we conclude the mean weight differs" instead of "we conclude the mean weight of cereal boxes differs from 16 oz."
• On CIs: rounding intermediate values too aggressively. Carry 3-4 decimals through, round only at the end.
• Picking the wrong inference procedure (e.g., 2-sample $t$ when it should be paired $t$).

What this 3-day plan deliberately skips

You will NOT relearn probability rules from scratch (geometric, binomial distributions). If you've forgotten them: skim the formulas, do 3 problems, and accept you may lose 4-6 points there. Spend the saved time on inference instead.

Ready to start?

Open the AP Statistics topic library → and start with whichever Day 1 topic you're weakest on. Mix in 3-5 worked examples per topic. Good luck — you've got this.