Do I pool proportions for a confidence interval?

No. A two-proportion confidence interval estimates each group’s variance separately. The usual equality test pools successes and sample sizes because its null hypothesis sets the population proportions equal.

Are chi-square tests part of the new Unit 3?

Yes. Topics 3.14 and 3.15 cover chi-square tests for homogeneity or independence. The revised unit has 15 topics. An older resource’s Unit 8 numbering does not match the 2026–27 course.

Which calculator can I use on AP Statistics in 2027?

A graphing calculator with statistical capabilities is expected on both sections. Bluebook includes Desmos graphing. Nongraphing handheld calculators are not allowed in 2027.

AP Statistics

AP Statistics Unit 3 review: Inference for Categorical Data: Proportions

Unit 3 estimates and tests population proportions and compares categorical distributions. It is 15–25% of multiple choice in the revised course. Expect to choose an inference method, verify numerical conditions, calculate results and state a conclusion about the population rather than just the sample.

Try the practice questions Topic list

By Marteen Tang, founder of Ashore · Updated Nov 9, 2026 · Sources at the bottom of the page

Unit 3 on the May 2027 exam

AP Statistics Unit 3 exam facts
	2027 exam
Weight	15–25% of the multiple-choice section
Exam date	Tuesday, May 11, 2027, afternoon session
Multiple choice	42 questions in 90 minutes, worth 50% of the exam score
Free response	4 questions in 90 minutes, worth 50%. All answers are entered in Bluebook: two multi-focus questions, one inference question and a final multi-focus question.
Calculator	A graphing calculator with statistical capabilities is expected on both sections. Bluebook includes Desmos graphing. Nongraphing handheld calculators are not allowed in 2027.
Class time	About 30 class periods in College Board's pacing guide
2026 results	17% of students scored a 5 on the whole exam, and about 62% scored 3 or higher

Sources: College Board's course and exam description, exam page, 2027 exam dates and score distributions.

What Unit 3 covers

College Board's course description splits the unit into 15 topics. The second column is what you should be able to do for each one.

AP Statistics Unit 3 topics
Topic	What you should be able to do
3.1 Estimators	Explain estimator bias and variability across repeated samples.
3.2 Sampling Distributions for Sample Proportions	Calculate the center and spread of a sample-proportion distribution and check normal approximation conditions.
3.3 Constructing a Confidence Interval for a Population Proportion	Construct a one-proportion z interval with an estimated standard error.
3.4 Justifying a Claim Based on a Confidence Interval for a Population Proportion	Interpret an interval and its confidence level and evaluate a population claim.
3.5 Setting Up a Test for a Population Proportion	Define the population proportion, state hypotheses and check conditions for a one-proportion test.
3.6 p-Values	Interpret a p-value as a conditional probability under the null hypothesis.
3.7 Carrying Out a Test for a Population Proportion	Calculate a one-proportion z statistic, p-value and contextual conclusion.
3.8 Potential Errors When Performing Tests	Distinguish Type I and Type II errors and explain power and significance level.
3.9 Sampling Distributions for the Difference Between Sample Proportions	Describe the sampling distribution of a difference between independent sample proportions.
3.10 Constructing a Confidence Interval for the Difference Between Two Population Proportions	Construct a two-proportion interval using an unpooled standard error.
3.11 Justifying a Claim Based on a Confidence Interval for the Difference Between Two Population Proportions	Interpret the interval for a difference with a consistent subtraction order.
3.12 Setting Up a Test for the Difference Between Two Population Proportions	State hypotheses and check conditions for a two-proportion test.
3.13 Carrying Out a Test for the Difference Between Two Population Proportions	Calculate a two-proportion test using the pooled estimate under equal population proportions.
3.14 Setting Up a Chi-Square Test for Homogeneity or Independence	Choose a chi-square test for homogeneity or independence and calculate expected counts.
3.15 Carrying Out a Chi-Square Test for Homogeneity or Independence	Calculate a chi-square statistic, degrees of freedom, p-value and contextual conclusion.

Inference conditions and standard errors for categorical data

Use random samples or a randomized design as required by the procedure. When sampling without replacement, check each sample is at most 10% of its population.

Inference conditions and standard errors for categorical data
Procedure	Large-count check	Standard error or expected counts
One-proportion interval	Observed successes and failures each at least 10	SE = √(p̂(1 − p̂)/n).
One-proportion test	Expected np₀ and n(1 − p₀) each at least 10	Null SD = √(p₀(1 − p₀)/n).
Two-proportion interval	At least 10 observed successes and failures in each independent sample	SE = √(p̂₁(1 − p̂₁)/n₁ + p̂₂(1 − p̂₂)/n₂).
Two-proportion equality test	Check expected successes and failures in both groups under pooled p̂	p̂pool = (x₁ + x₂)/(n₁ + n₂); use it in both variance terms.
Chi-square independence or homogeneity	Every expected cell count at least 5	Expected = row total × column total / grand total.
Chi-square statistic	Independent counts in categories	χ² = Σ(O − E)²/E; df = (rows − 1)(columns − 1).

Common mistakes

Each of these loses points on questions you otherwise understand.

Writing only “random” or “large sample” as a condition check. Identify the sampling method and show the relevant counts. CED printed p. 81.
Treating 95% confidence as the probability that a fixed parameter moves into this computed interval. Confidence describes the long-run coverage of the method. CED pp. 81–82.
Accepting the null after a large p-value. State that evidence is insufficient to reject it. CED p. 82.
Checking observed rather than expected counts for a chi-square test. The condition is about every expected count being at least 5. CED p. 82.

6 practice questions with answers

Written by Ashore for this page, in the style of the multiple-choice section. Try each one before you open the answer.

Question 1 · 3.3
A random sample of 400 from a population above 10,000 gives 144 successes. What is the estimated standard error of p̂?
- A0.048
- B0.024
- C0.030
- D0.000576
Show the answer
B. p̂ = 144/400 = 0.36. SE = √(0.36 × 0.64/400) = √0.000576 = 0.024. There are 144 successes and 256 failures, and the sampling fraction is below 10%.
Question 2 · 3.3
For that sample, use p̂ = 0.36, SE = 0.024 and z* = 1.96. What is the approximate 95% confidence interval?
- A(0.336, 0.384)
- B(0.264, 0.456)
- C(0.350, 0.370)
- D(0.313, 0.407)
Show the answer
D. The margin is 1.96(0.024) = 0.04704. The endpoints are 0.31296 and 0.40704. The interval estimates the population proportion, not the proportion of individual outcomes inside a range.
Question 3 · 3.7
For a test of H₀: p = 0.40, a random sample of 200 from a large population gives 98 successes. What is the z statistic?
- A2.60
- B1.80
- C0.90
- D3.67
Show the answer
A. p̂ = 0.49. The null SD is √(0.40 × 0.60/200) ≈ 0.03464. z = (0.49 − 0.40)/0.03464 ≈ 2.60. Use p₀ in the test denominator, not p̂.
Question 4 · 3.13
Two independent samples have 45 successes out of 150 and 84 out of 210. What pooled proportion is used to test p₁ = p₂?
- A0.3500
- B0.3000
- C0.3583
- D0.4000
Show the answer
C. Pool the counts, not the percentages: (45 + 84)/(150 + 210) = 129/360 = 0.3583. A simple mean of 0.30 and 0.40 ignores the different sample sizes.
Question 5 · 3.14
A cell in a two-way table belongs to a row totaling 90 and a column totaling 80. The grand total is 240. What expected count is used under independence?
- A45
- B30
- C80
- D170
Show the answer
B. Expected count = 90 × 80/240 = 30. This is a model-based count under independence and can differ from the observed count in that cell.
Question 6 · 3.15
A chi-square independence test uses a table with 3 rows and 4 columns. What are its degrees of freedom?
- A12
- B7
- C9
- D6
Show the answer
D. df = (r − 1)(c − 1) = (3 − 1)(4 − 1) = 6. The formula reflects constraints imposed by the row and column totals.

How to study Unit 3

Sort problems by the number of populations, the response type and whether the goal is an interval or a test. Define p or p₁ − p₂ in words before writing a formula. Show the actual success/failure counts or expected cell counts in the condition check.

After calculating a p-value, compare it numerically with α and write a sentence about the population claim. Practice distinguishing a p-value interpretation from a confidence-level interpretation. For two groups, keep the same subtraction order in the hypotheses, statistic and conclusion.

Ashore's Stats course has a lesson and practice questions for every topic in this unit. The free starting check takes about 15 minutes and shows which ones are costing you points.

Questions

Still have a question? support@tryashore.com

It is 15–25% of the multiple-choice section, which is half the exam score. This is not a fixed share of the whole exam: free-response questions can combine units. Suggested pacing is 30 class periods.

By Marteen Tang · Founder of Ashore

Marteen Tang founded Ashore and works on its SAT and AP lessons, practice and plans. Updated Nov 9, 2026.

Sources

Find the Stats topics costing you points

The starting check takes about 15 minutes. Free, no card.

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SAT Math · 1 of 5

Calculator allowed

A jacket's price is increased by 20% and then the new price is decreased by 20%. The final price is what percent of the original price?

A $96\%$
B $100\%$
C $104\%$
D $80\%$