• 54 questions

AP Stats Unit 3 Practice Test

Unofficial practice for Unit 3 of AP Statistics, inference for proportions, as revised for 2026-27.

An estimator is unbiased when, on average, its value does what?

Pick an answer, then press Check answer. Then you see Correct or Not quite, with the reason. Keys: A to D pick, Enter checks.

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Unofficial practice questions, not affiliated with the College Board. Bank checked October 14, 2026.

All 54 questions

Topics 3.1 and 3.2: Estimators and sample proportions 4

  • The 10% condition asks that the population be at least 10 times as large as the sample. When is it needed? College Board, AP Statistics Course and Exam Description, topic 3.2, essential knowledge 3.2.B.1
  • An estimator is unbiased when, on average, its value does what? College Board, AP Statistics Course and Exam Description, topic 3.1, essential knowledge 3.1.A.1
  • In 84 of 200 randomly chosen households, someone owns a bicycle. What is the sample proportion called when it is used to estimate the proportion for all households? College Board, AP Statistics Course and Exam Description, topic 3.1, essential knowledge 3.1.B.1
  • In a town, 25% of households have a dog. For random samples of 300 households, what is the standard deviation of the sampling distribution of the sample proportion? College Board, AP Statistics Course and Exam Description, topic 3.2, essential knowledge 3.2.A.1
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Topics 3.3 and 3.4: Confidence interval for a proportion 11

  • A 95% confidence interval for the proportion of a city's adults who bike to work is (0.12, 0.18). Which interpretation is right? College Board, AP Statistics Course and Exam Description, topic 3.4, essential knowledge 3.4.A.3
  • A company says that half of its customers prefer a new label. A 95% confidence interval from a random sample of customers is (0.41, 0.48). What does the interval suggest about the claim? College Board, AP Statistics Course and Exam Description, topic 3.4, essential knowledge 3.4.B.1
  • A confidence interval for a population proportion runs from 0.31 to 0.39. What is its margin of error? College Board, AP Statistics Course and Exam Description, topic 3.3, essential knowledge 3.3.D.3
  • A poll of 400 people is repeated with 1,600 people, at the same confidence level and with about the same sample proportion. About how wide is the new interval next to the old one? College Board, AP Statistics Course and Exam Description, topic 3.4, essential knowledge 3.4.C.2
  • A pollster wants to estimate the proportion of all voters in a city who favor a ballot measure, using one random sample. Which procedure fits? College Board, AP Statistics Course and Exam Description, topic 3.3, essential knowledge 3.3.A.1
  • A researcher wants a margin of error of 0.05 at 95% confidence (critical value 1.96) and has no earlier estimate of the proportion. What is the smallest sample size that will do? College Board, AP Statistics Course and Exam Description, topic 3.3, essential knowledge 3.3.D.4
  • For one sample, the confidence level is raised from 90% to 99%. What happens to the confidence interval? College Board, AP Statistics Course and Exam Description, topic 3.4, essential knowledge 3.4.C.1
  • In a random sample of 80 customers, 6 return an item. Is the normality condition met for a one-sample z-interval for the proportion who return an item? College Board, AP Statistics Course and Exam Description, topic 3.3, essential knowledge 3.3.B.1.iii
  • In a random sample of 150 students, 60% say they eat breakfast, and the standard error is 0.04. With a critical value of 1.96, what is the 95% confidence interval for the population proportion? College Board, AP Statistics Course and Exam Description, topic 3.3, essential knowledge 3.3.C.2
  • In a random sample of 150 students, 60% say they eat breakfast. What is the standard error of the sample proportion? College Board, AP Statistics Course and Exam Description, topic 3.3, essential knowledge 3.3.D.1
  • What does a confidence level of 95% say about the method that produced an interval for a population proportion? College Board, AP Statistics Course and Exam Description, topic 3.4, essential knowledge 3.4.A.2

Topics 3.5 to 3.7: Test for a proportion 11

  • A city says that 30% of its households recycle. A citizens' group believes the true proportion is higher and takes a random sample. Which hypotheses fit? College Board, AP Statistics Course and Exam Description, topic 3.5, essential knowledge 3.5.B.3
  • A coin is tested for fairness, with no idea beforehand of which way it might lean. Which alternative hypothesis fits? College Board, AP Statistics Course and Exam Description, topic 3.5, essential knowledge 3.5.B.2
  • A null distribution is simulated 1,000 times for a test with the alternative p > p0. In 38 of the simulations the statistic is at or above the observed value. What is the p-value? College Board, AP Statistics Course and Exam Description, topic 3.6, essential knowledge 3.6.A.2
  • A test of H0: p = 0.4 against Ha: p ≠ 0.4 gives a p-value of 0.012. The researcher set a significance level of 0.01 beforehand. What is the formal decision? College Board, AP Statistics Course and Exam Description, topic 3.7, essential knowledge 3.7.B.2
  • A test of H0: p = 0.5 uses a random sample of 100, and the sample proportion is 0.58. What is the z test statistic? College Board, AP Statistics Course and Exam Description, topic 3.7, essential knowledge 3.7.A.1
  • A transit agency tests H0: p = 0.10 against Ha: p > 0.10 for the proportion of its buses that run late. The p-value is 0.21 and the significance level is 0.05. Which conclusion is right? College Board, AP Statistics Course and Exam Description, topic 3.7, essential knowledge 3.7.B.4
  • A two-sided test gives z = 2.0, and the area above 2.0 under the standard normal curve is 0.0228. What is the p-value? College Board, AP Statistics Course and Exam Description, topic 3.6, essential knowledge 3.6.A.1.iii
  • In a significance test, which hypothesis holds the researcher's claim or belief about the parameter? College Board, AP Statistics Course and Exam Description, topic 3.5, essential knowledge 3.5.B.1
  • In a test about a population proportion, what does the p-value measure? College Board, AP Statistics Course and Exam Description, topic 3.6, essential knowledge 3.6.A.1
  • In a test of H0: p = 0.20, a random sample of 60 has 18 successes. Which counts does the normality condition for the test check? College Board, AP Statistics Course and Exam Description, topic 3.5, essential knowledge 3.5.C.1.iii
  • What does a small p-value indicate? College Board, AP Statistics Course and Exam Description, topic 3.6, essential knowledge 3.6.A.4

Topic 3.8: Type I and Type II errors 7

  • A new page layout really does raise the proportion of visitors who sign up, but a test of the two layouts fails to find convincing evidence of it. Which error was made? College Board, AP Statistics Course and Exam Description, topic 3.8, essential knowledge 3.8.A.2
  • A test finds convincing evidence that more than 5% of a factory's parts are flawed. In truth, exactly 5% are. Which error was made? College Board, AP Statistics Course and Exam Description, topic 3.8, essential knowledge 3.8.A.1
  • Before collecting data, a researcher sets the significance level of a test at α = 0.10. Which probability does that choice fix? College Board, AP Statistics Course and Exam Description, topic 3.8, essential knowledge 3.8.B.1
  • For one alternative value of the parameter, the probability of a Type II error is 0.15. What is the power of the test against that alternative? College Board, AP Statistics Course and Exam Description, topic 3.8, essential knowledge 3.8.B.2
  • In a study where a Type I error would have very serious consequences, what should the researcher choose before collecting data? College Board, AP Statistics Course and Exam Description, topic 3.8, essential knowledge 3.8.D.2
  • What is the power of a significance test? College Board, AP Statistics Course and Exam Description, topic 3.8, essential knowledge 3.8.A.3
  • With everything else unchanged, which change increases the power of a test? College Board, AP Statistics Course and Exam Description, topic 3.8, essential knowledge 3.8.C.1

Topics 3.9 to 3.13: Two proportions 11

  • A 95% confidence interval for p1 − p2 is (−0.03, 0.09). What does it suggest? College Board, AP Statistics Course and Exam Description, topic 3.11, essential knowledge 3.11.B.1
  • A 95% confidence interval for the proportion of commuters who ride the bus in City A minus the proportion in City B is (0.04, 0.16). What does it suggest? College Board, AP Statistics Course and Exam Description, topic 3.11, essential knowledge 3.11.B.1
  • From independent random samples of teens and of adults, researchers want to estimate how much larger the proportion who use a certain app is among teens. Which procedure fits? College Board, AP Statistics Course and Exam Description, topic 3.10, essential knowledge 3.10.A.1
  • In one group, 36 of 120 people succeed; in a second group, 44 of 80 succeed. What is the combined (pooled) proportion for a two-sample z-test? College Board, AP Statistics Course and Exam Description, topic 3.13, essential knowledge 3.13.A.1
  • In one random sample, 62 of 100 people say yes. In an independent random sample, 90 of 200 say yes. What is the point estimate of p1 − p2? College Board, AP Statistics Course and Exam Description, topic 3.10, essential knowledge 3.10.C.1
  • Seeds are randomly assigned to a new or an old fertilizer. A test of H0: p1 = p2 against Ha: p1 > p2, with p1 for the new fertilizer, gives a p-value of 0.008. At a significance level of 0.05, which conclusion is right? College Board, AP Statistics Course and Exam Description, topic 3.13, essential knowledge 3.13.C.3
  • Two independent random samples of 100 give sample proportions of 0.60 and 0.40, so the combined proportion is 0.50. What is the z test statistic for the difference? College Board, AP Statistics Course and Exam Description, topic 3.13, essential knowledge 3.13.A.1
  • Two independent random samples of 200 give sample proportions of 0.60 and 0.50. With a critical value of 1.96, what is the margin of error of a 95% confidence interval for the difference? College Board, AP Statistics Course and Exam Description, topic 3.10, essential knowledge 3.10.D.2
  • Volunteers are randomly assigned to two treatments, and the proportions who improve are compared with a two-sample z-interval. Which of the usual conditions is unnecessary? College Board, AP Statistics Course and Exam Description, topic 3.10, essential knowledge 3.10.B.1.ii
  • What does the null hypothesis say in a two-sample z-test for the difference between two population proportions? College Board, AP Statistics Course and Exam Description, topic 3.12, essential knowledge 3.12.B.1
  • Why does the two-sample z-test for a difference in proportions use a combined proportion in its standard error? College Board, AP Statistics Course and Exam Description, topic 3.12, essential knowledge 3.12.C.1.iii

Topics 3.14 and 3.15: Chi-square tests 10

  • A chi-square test for independence between grade level and club membership at a school gives a p-value of 0.31, with a significance level of 0.05. Which conclusion is right? College Board, AP Statistics Course and Exam Description, topic 3.15, essential knowledge 3.15.D.3
  • A two-way table has an expected count of 3.2 in one cell. Which condition for a chi-square test fails? College Board, AP Statistics Course and Exam Description, topic 3.14, essential knowledge 3.14.D.1.iii
  • As the degrees of freedom of a chi-square distribution increase, what happens to its skew? College Board, AP Statistics Course and Exam Description, topic 3.14, essential knowledge 3.14.A.2
  • The counts for a chi-square test fill a two-way table with 2 rows and 5 columns. How many degrees of freedom does the test have? College Board, AP Statistics Course and Exam Description, topic 3.15, essential knowledge 3.15.B.1
  • In a two-way table with 200 observations, one cell sits in a row with total 60 and a column with total 50. What is its expected count under the null hypothesis? College Board, AP Statistics Course and Exam Description, topic 3.15, essential knowledge 3.15.A.1
  • Independent random samples of students from three schools are each asked to pick a favorite of four lunch options. Which test compares the three distributions? College Board, AP Statistics Course and Exam Description, topic 3.14, essential knowledge 3.14.B.1
  • One cell of a two-way table has an observed count of 30 and an expected count of 20. How much does it add to the chi-square statistic? College Board, AP Statistics Course and Exam Description, topic 3.15, essential knowledge 3.15.B.1
  • One random sample of 500 adults is taken, and each adult is classified by age group and by main news source. Which test asks whether the two variables are associated? College Board, AP Statistics Course and Exam Description, topic 3.14, essential knowledge 3.14.B.3
  • What is the null hypothesis of a chi-square test for independence? College Board, AP Statistics Course and Exam Description, topic 3.14, essential knowledge 3.14.C.2
  • What shape do chi-square distributions have? College Board, AP Statistics Course and Exam Description, topic 3.14, essential knowledge 3.14.A.2

How this list was compiled: Our own questions, written to Unit 3 (Inference for Categorical Data: Proportions, topics 3.1 to 3.15) of the College Board's AP Statistics Course and Exam Description, effective fall 2026, https://apcentral.collegeboard.org/media/pdf/ap-statistics-course-and-exam-description.pdf, read 2026-10-14. Each rule was read on 2026-10-14 in the essential knowledge statement named under its question, and every worked answer was recomputed from the numbers in its question. Licence: Own work.

How it works

This AP Stats Unit 3 practice test has 54 questions of our own on inference for proportions: confidence intervals, significance tests and chi-square tests. It is unofficial and not affiliated with the College Board, which owns AP.

Read the full guide

What Unit 3 covers now

AP Statistics was revised for the 2026-27 school year. The College Board's course description, effective fall 2026 and read October 14, 2026, names Unit 3 Inference for Categorical Data: Proportions and gives it fifteen topics. The bank takes them in order: estimators and sample proportions (4 questions), confidence intervals for one proportion (11), tests for one proportion (11), Type I and Type II errors (7), two proportions (11), and chi-square tests (10). The description weights no topic; the spread is ours.

Where each answer rests

Under every answer is the essential knowledge statement of the description that it rests on. The worked answers were each recomputed from the question's own numbers.

  • An interval checks the observed counts of successes and failures. A test checks the counts expected under the null value.
  • Never write "accept H0". A large p-value says only that the evidence for the alternative is not convincing.
  • Homogeneity compares several samples on one variable. Independence classifies one sample by two variables.

Questions and answers

What is Unit 3 in AP Stats?

Inference for Categorical Data: Proportions. The unit takes about 30 class periods and carries 15 to 25% of the multiple-choice section of the exam.

What should a Unit 3 AP Stats study guide cover?

The sampling distribution of a sample proportion, the one-sample z-interval and z-test, p-values, Type I and Type II errors and power, the two-sample procedures with their combined proportion, and the chi-square tests for homogeneity and independence, each with its three conditions.

Isn't AP Stats Unit 3 Collecting Data?

It was, in the earlier nine-unit course. The course revised for 2026-27 has five units, and sampling methods and experiments moved into Unit 1, Exploring One-Variable Data and Collecting Data.

How many questions are on the AP Stats Unit 3 Progress Check?

About 65 multiple-choice questions and 3 free-response questions, all three on inference, by the course description. Teachers assign it in AP Classroom.

Is this the real AP Stats Unit 3 test?

No. Each of the 54 questions was written for this page from the topics the course description lists. The College Board's questions are in AP Classroom and on its exams, and none is repeated here.