AP Statistics Unit 6: Inference for Categorical Data: Proportions

Unit 6 covers inference for proportions: confidence intervals and significance tests for one and two proportions. The conditions are not preamble — checking them is scored, and skipping them costs marks on the free-response section.

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107 questions10 CED topics100% with a figure
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What 107 questions on it look like

It spans 10 CED topics, which is wide enough that "I've studied this unit" is not a meaningful statement. Track your accuracy by topic, not by unit.

100% of the questions come with a figure — a graph, diagram or data display. Reading the figure correctly is most of the work before any content knowledge applies.

Potential Errors When Performing Tests37
Concluding a Test for a Population Proportion37
Setting Up a Test for a Population Proportion15
Constructing a Confidence Interval for a Population Proportion4
Justifying a Claim Based on a Confidence Interval for a Population Proportion4
Interpreting p-Values3
Setting Up a Test for the Difference of Two Population Proportions3
Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions2

Questions per CED topic, top 8 of 10.

From the bank

Three real inference for categorical data: proportions questions

Drawn from the practice pool, not from the mock papers.

Justifying a Claim Based on a Confidence Interval for a Population Proportion · Statistical Argumentation · with figure

A random sample of county voters gives a 95% confidence interval of (0.56, 0.68) for the proportion of all county voters who support adding protected bike lanes. Which interpretation is correct?

  1. AExactly 95% of county voters have support levels between 0.56 and 0.68.
  2. BThe P-value gives the probability that the null hypothesis is true after the sample has been observed.
  3. CThere is a 95% probability that the sample proportion is between 0.56 and 0.68.
  4. DThe method used to make the interval captures the true countywide support proportion in about 95% of repeated random samples.correct
  5. EIf the same sample were surveyed again, the interval would be the same 95% of the time.
Why D is correct

A confidence level describes the long-run success rate of the interval method. The parameter is the fixed countywide support proportion, and the interval (0.56, 0.68) is one estimate from one random sample.

Confidence interval interpretation for a proportion: in the "A random sample of county voters gives a 95% confidence interval of (0.56, 0.68) for the proportion of all county voters who support adding protected bike lanes. Which interpretation is correct?" setting, especially proportion of county voters who support adding protected bike lanes, build the interval with the correct standard error and interpret it in context. The professional check is to keep the values 95%, 0.56, 0.68, 0.95, the confidence interval interpretation method, and the final answer choice aligned with Inference for Categorical Data: Proportions.

Common mistakes. For the stem cue "A random sample of county voters gives a ninety five percent confidence interval of (zero point five six, zero point six eight) for the proportion of all county voters who support adding", a likely mistake is the sample proportion is known once the sample is observed; the interval estimates the population proportion. Keep the calculation or conclusion tied to the original context.

Concluding a Test for a Population Proportion · Statistical Argumentation · with figure

A one-proportion z test based on a random sample with test conditions satisfied is performed for H0: p = 0.40 versus Ha: p > 0.40. The p-value is 0.018. At significance level 0.05, which conclusion is appropriate?

  1. AFail to reject H0 because 0.018 is less than 0.05.
  2. BReject H0; there is convincing evidence that the population proportion equals 0.40.
  3. CThe P-value or confidence level is the probability that the null hypothesis is true after the sample is observed.
  4. DFail to reject H0; the sample proves the population proportion is less than 0.40.
  5. EReject H0; there is convincing evidence that the population proportion is greater than 0.40.correct
Why E is correct

Because the p-value 0.018 is less than alpha = 0.05, reject H0. The alternative is p > 0.40, so the conclusion must state evidence that the population proportion is greater than 0.40.

One-proportion test conclusion: in the "A one-proportion z test based on a random sample with test conditions satisfied is performed for H0: p = 0.40 versus Ha: p > 0.40. The p-value is 0.018. At significance level 0.05, which conclusion is appropriate?" setting, especially greater, state the hypotheses, compute the relevant test evidence, and conclude in context. The professional check is to keep the values 0, 0.40, 0.018, 0.05, 0.4, the hypothesis test conclusion method, and the final answer choice aligned with Inference for Categorical Data: Proportions.

Common mistakes. For the stem cue "A one-proportion z test based on a random sample with test conditions satisfied is performed for Hzero: p = zero point four zero versus Ha: p > zero point four zero.", a likely mistake is rejecting H0 does not provide evidence that the null value is true. Keep the calculation or conclusion tied to the original context.

Setting Up a Test for a Population Proportion · Selecting Statistical Methods · with figure

A study tests greater than 0.40 for proportion of reusable cup users. Which hypotheses use the correct parameter?

  1. AH0: p-hat = p0; Ha: p-hat != p0
  2. BH0: p = 0.40; Ha: p > 0.40correct
  3. CH0: p > 0.40; Ha: p = 0.40
  4. DH0: sample statistic = 0; Ha: sample statistic differs
  5. EH0: p-hat = 0; Ha: x-bar != 0
Why B is correct

The hypotheses should be H0: p = 0.40 and Ha: p > 0.40.

hypotheses for proportion of reusable cup users: in the "A study tests greater than 0.40 for proportion of reusable cup users. Which hypotheses use the correct parameter?" setting, especially proportion of reusable cup users; p; p = 0.40, state the hypotheses, compute the relevant test evidence, and conclude in context. The professional check is to keep the values 0.40, the hypothesis setup method, and the final answer choice aligned with Inference for Categorical Data: Proportions.

Common mistakes. For the stem cue "A study tests greater than zero point four zero for proportion of reusable cup users. Which hypotheses use the correct parameter?", a likely mistake is hypotheses should use population parameters, not sample statistics. Keep the calculation or conclusion tied to the original context.

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FAQ

Inference for Categorical Data: Proportions questions

What does a 95% confidence interval mean?

That the method captures the true parameter in 95% of samples. It is not a 95% probability that this particular interval contains it.

What is a Type I error?

Rejecting a true null hypothesis. A Type II error is failing to reject a false one.
Last reviewed 2026-08-28. Unit and topic names follow the College Board course framework. Question counts describe the PrepScore practice bank, not the exam.
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2 of this unit’s topics have enough practice questions for a page of their own.

Concluding a Test for a Population Proportion37 questionsPotential Errors When Performing Tests37 questions
Same course
Unit 1: Exploring One-Variable Data460 questionsUnit 2: Exploring Two-Variable Data295 questionsUnit 3: Collecting Data190 questionsUnit 4: Probability, Random Variables, and Probability Distributions100 questionsUnit 5: Sampling Distributions70 questionsUnit 7: Inference for Quantitative Data: Means63 questionsUnit 9: Inference for Quantitative Data: Slopes133 questions

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