AP Statistics — t procedures for one mean and paired data

This material trains the first half of Unit 4 of the AP Statistics course framework for 2026–27, Inference for Quantitative Data: Means, at the level of an introductory college statistics course and with a graphing calculator in hand. It covers the sampling distribution of a sample mean and the t procedures for a single population mean and for a population mean difference from matched pairs.

The quiz moves through the skills one at a time. You use the central limit theorem to find a probability about a sample mean; explain why a t-distribution with $n-1$ degrees of freedom replaces the normal model when the sample standard deviation stands in for the population one; choose the right critical value; decide whether the sample data condition holds for a small sample with an outlier; compute a one-sample t-interval and say how sample size and confidence level change its width; recognize a before-and-after design as matched pairs and analyze it as one sample of differences; write hypotheses about the population mean difference; compute a paired t statistic with the correct degrees of freedom; interpret a p-value and a confidence interval for a mean difference; and use an interval to judge a claim about a mean. Every question carries its own numbers, and each explanation shows the working and why the other answers go wrong.

The flashcards review the formulas, the three conditions in the course's wording (randomization, 10% and sample data), the shape of t-distributions and the standard interpretations.

The written work is a printable sheet of eight free-response tasks modeled on the inference question of the exam: a full t-interval with conditions and interpretation, a complete paired t-test from raw differences, the reason pairing matters, the central limit theorem for a skewed population, the behavior of t critical values, judging a battery-life claim with an interval, a one-sided test at the 1 percent level, and the effect of confidence level and sample size on the margin of error. Handwritten answers are photographed and checked against model answers and key points.

The oral exam has an examiner ask one question at a time, from recognizing the design and naming the procedure to computing, interpreting and concluding, and it closes with short, precise feedback.

Two-sample t procedures for independent groups are treated in a separate material of this category. All scenarios are invented and all questions are original practice items written by Zestly, not released exam questions. The material follows the published course framework but is independent practice and does not predict an exam score.

• Describe the sampling distribution of a sample mean and use the central limit theorem to find probabilities
• Explain when and why t procedures with $n - 1$ degrees of freedom are used, and choose critical values
• Check the randomization, 10% and sample data conditions for one-sample and paired t procedures
• Construct and interpret a one-sample t-interval and explain how sample size and confidence level affect its width
• Recognize a matched-pairs design and carry out a paired t-test on the differences
• Interpret p-values and intervals for a mean or mean difference and use an interval to judge a claim

Practice material written by Zestly, based on the College Board AP Statistics course framework effective fall 2026 (Unit 4, Inference for Quantitative Data: Means, topics 4.1–4.5). Original questions, not released exam items.