How to use the simulator
Each card asks one question; click an answer to move on.
- Step 1: What kind of data? Categorical (counts or proportions) or Quantitative (numbers or means).
- Categorical, then How many samples (groups)? 1 sample, 2 independent samples, or More categories or a two-way table. The last choice adds a question: are the distributions the same across groups, or are two categorical variables associated?
- Quantitative, then How many samples (groups)? 1 sample, 2 independent samples, or 2 paired samples.
The final card, headed You should use, names one of seven procedures: One-Proportion z, Two-Proportion z, Chi-Square Test of Homogeneity, Chi-Square Test of Independence, One-Sample t, Two-Sample t or Matched-Pairs t. It also shows a one-line description of when the procedure applies, the Test statistic formula, a list of Conditions to check and a Conclusion / interval phrasing template.
Above the card, Your path so far lists each question with your answer. The Full tree overview map beside it shows the whole tree, with your path in teal and your current position in gold. There is no back button, so press Start over to change an earlier answer.
The tree leaves out chi-square goodness-of-fit and inference for the slope of a regression line. Neither is part of the course framework that takes effect in fall 2026.
The key ideas
Three questions settle almost every choice:
- What type of variable is the response? Categorical data lead to proportions (z) or chi-square. Quantitative data lead to means (t).
- How many samples or groups? One group is compared with a claimed value. Two groups are compared with each other. Three or more groups, or two categorical variables, need chi-square.
- Independent or paired? If the same subjects are measured twice, or subjects are deliberately matched, analyse the differences with a one-sample t procedure on those differences.
Two more decisions finish the job. Does the question ask you to estimate a parameter (confidence interval) or to test a claim (significance test)? And for two-way tables, how were the data collected? Separate samples from two or more populations call for homogeneity. One sample classified on two variables calls for independence.
Whatever the procedure, the write-up follows the same four steps: State the parameter and hypotheses (or confidence level), Plan by naming the procedure and checking conditions (Random, 10%, and Large Counts or Normal/Large Sample), Do the calculation, and Conclude in context.
Worked example
Problem: In a random sample of 400 voters in a city, 228 support a new transit tax. At α = 0.05, is there convincing evidence that a majority of the city's voters support the tax?
Choose the procedure. Each voter answers yes or no, so the data are categorical, and there is one sample compared with a claimed value. The path is Categorical, then 1 sample, which ends at the One-Proportion z-Test.
State. and , where is the proportion of all voters in the city who support the tax.
Plan. The sample is random. 400 is less than 10% of the city's voters. Large Counts: and , both at least 10.
Do. . , so the P-value is .
Conclude. Because 0.0026 < 0.05, reject H0. There is convincing evidence that a majority of the city's voters support the transit tax.
A contrasting case: 20 patients have blood pressure measured before and after taking a drug. The response is quantitative, and each patient gives two linked measurements, so the path is Quantitative, then 2 paired samples, which ends at the Matched-Pairs t-Test on the 20 differences, with df = 19.
Common mistakes on the AP exam
- Using two-sample t on paired data. Before-and-after measurements on the same subjects, or twins and matched pairs, are not independent samples.
- Using z for means or t for proportions. Means with s use t; proportions use z.
- Naming the procedure vaguely. "t-test" is not enough. Write "one-sample t-test for a population mean" or "two-proportion z-interval for p1 − p2".
- Mixing up homogeneity and independence. The arithmetic is the same, but the hypotheses and the sampling design differ, so the name must match how the data were collected.
- Using the wrong value in Large Counts. A one-proportion test checks np0 and n(1 − p0). An interval checks with p̂. Chi-square needs every expected count to be at least 5.
- Listing conditions without evidence. "Normal ✓" earns little. Say why: n = 40 ≥ 30, or the dotplot of differences shows no strong skew or outliers.
- Concluding without context, or "accepting" H0. State the conclusion about the parameter in the problem's words, and say "fail to reject" rather than "accept".
When the AP exam uses this
Choosing the procedure is the first step of every inference question in Unit 3 (proportions and chi-square) and Unit 4 (means). On free-response questions, naming the correct procedure and checking its conditions is part of the scoring, and the calculation and conclusion that follow depend on that choice.