AP Statistics — inference for one proportion

This material trains the core inference skills of Unit 3 of the AP Statistics course framework for 2026–27: working with the sampling distribution of a sample proportion and then estimating and testing a single population proportion. It is written for students preparing for the May 2027 exam at the level of an introductory college statistics course, with a graphing calculator at hand.

The quiz works through the full chain one step at a time. You find the mean and standard deviation of the sampling distribution of p^ and use the normal model to find a probability; decide which condition fails in a described situation, using the course's randomization, 10% and normality conditions and the difference between observed counts for an interval and expected counts for a test; compute a 95 percent one-sample z-interval from counts and the sample size needed for a chosen margin of error; interpret an interval correctly and use it to judge a claim; write hypotheses about the parameter rather than the statistic; compute a z test statistic with the null value in the standard error; interpret a p-value as a probability computed assuming the null hypothesis; state a conclusion in context without claiming proof; and describe a Type II error in context. Every question carries its own numbers and a full worked explanation.

The flashcards collect the formulas, the three conditions and the standard interpretations of a confidence level, a p-value and the two error types.

The written work is a printable sheet of eight free-response tasks in the style of the inference question of the exam: a complete confidence interval with conditions and interpretation, a complete significance test, a sample-size calculation with and without a prior estimate, the meaning of a p-value at two significance levels, the consequences of Type I and Type II errors in a food-safety setting, a probability from the sampling distribution of p^, and the use of an interval to evaluate a majority claim. Answers are handwritten, photographed and checked against model answers and key points, so the habits that earn credit, such as naming the procedure, checking conditions with numbers and concluding in context, are practiced on paper.

The oral exam puts you in front of an examiner who asks one question at a time about a survey, from choosing the procedure and checking conditions to interpreting the result and discussing errors, and ends with short, precise feedback.

All scenarios are invented, and all questions are original practice items written by Zestly; they are not taken from released exam material. The material follows the published course framework but is independent practice and does not predict an exam score.

  • Find the mean and standard deviation of the sampling distribution of a sample proportion and use the normal model for probabilities
  • Check the randomization, 10% and normality conditions for one-proportion inference, using observed counts for an interval and expected counts for a test
  • Construct and interpret a one-sample z-interval for a proportion and plan a sample size for a margin of error
  • Use a confidence interval to judge a claim about a population proportion
  • State hypotheses, compute a z test statistic and interpret a p-value for a one-sample z-test
  • Write conclusions in context and describe Type I and Type II errors and their consequences

Practice material written by Zestly, based on the College Board AP Statistics course framework effective fall 2026 (Unit 3, Inference for Categorical Data: Proportions, topics 3.1–3.8). Original questions, not released exam items.

Sample question

A regional power company reports that 22 percent of the households it serves are enrolled in paperless billing. An analyst selects a random sample of 150 of its roughly 90,000 households. What are the mean and the standard deviation of the sampling distribution of the sample proportion $\hat{p}$ of enrolled households?

See the answer

Mean 0.22, standard deviation about 0.034

The mean of $\hat{p}$ equals the population proportion, 0.22. Its standard deviation is $\sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.22 \times 0.78}{150}} = \sqrt{0.001144} \approx 0.034$. The value 0.0011 is the variance (the square root was not taken), 0.414 is $\sqrt{p(1-p)}$ without dividing by $n$, and 33 with 5.07 describes the COUNT of enrolled households, not the proportion.

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