AP Statistics Unit 6 Test: Inference for Categorical Data — Proportions

What Unit 6 Covers in AP Statistics

Unit 6 introduces formal statistical inference using the z-distribution for proportions. It is where the theoretical groundwork from Units 4 and 5 becomes a practical tool for drawing conclusions about categorical data from samples.

One-Sample z-Test for a Proportion

The one-sample z-test is used to test a claim about a single population proportion. The null hypothesis specifies a particular value for the population proportion, and the test statistic measures how many standard errors the sample proportion falls from that hypothesized value. The p-value gives the probability of observing a result at least as extreme as the one obtained, assuming the null hypothesis is true.

One-Sample Confidence Interval for a Proportion

A confidence interval for a population proportion provides a range of plausible values. The interval is calculated as the sample proportion plus or minus a critical z-value times the standard error. Interpretation must always be in context: a 95% confidence interval does not mean there is a 95% probability that the true parameter is in this particular interval — it means the method produces intervals that capture the true parameter 95% of the time in repeated sampling.

Two-Sample z-Tests and Confidence Intervals for Proportions

When comparing two population proportions, the two-sample z-procedure tests whether the difference between the two proportions equals zero (or some other specified value). The conditions must be verified for both samples separately before proceeding with the calculation.

The AP FRQ Four-Step Structure for Inference

AP Statistics FRQs on inference are scored using a four-step framework that must be followed explicitly:

1. State: Define the parameter(s) in context and state the null and alternative hypotheses using correct notation.
2. Plan: Identify the appropriate inference procedure and verify all required conditions (Random, Normal/Large Counts, and Independence/10%).
3. Do: Calculate the test statistic and p-value (or the confidence interval).
4. Conclude: Write a conclusion in context, referencing the p-value or interval, and linking back to the original question.

Key AP Exam Skills for Unit 6

• Writing hypotheses using correct parameter notation (p, not p-hat)
• Verifying the Random, 10%, and Large Counts conditions with specific numbers from the problem
• Interpreting the p-value correctly without saying 'the probability the null hypothesis is true'
• Writing a conclusion that states a decision about the null hypothesis and answers the original question in context
• Interpreting a confidence interval in the context of the problem

Frequent Unit 6 FRQ Errors

Stating Hypotheses About the Sample Statistic

Hypotheses must be written in terms of the population parameter p, not the sample proportion p-hat. Writing 'H0: p-hat = 0.5' is incorrect and costs points on the AP exam.

Incomplete Condition Verification

Stating that the conditions are met without showing the actual numerical check — for example, calculating np and n(1−p) and confirming both are at least 10 — does not earn full credit. Every condition check must include numbers from the problem.