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Statistics · AP · Inference for Categorical Data — Proportions

What this topic is

In Statistics · AP, this CED topic focuses on: Confidence Intervals for the Difference of Two Proportions. In plain terms, students should be able to explain the main idea in their own words and complete a straightforward practice item with justification.

This topic is assessed on the AP Exam.

Why it matters

• Inference write-ups are scored on conditions, mechanics, and contextual conclusions together.
• Inference for proportions (intervals and tests) is a large AP Stats exam block.
• Students must state hypotheses, check conditions, compute, and conclude in context.
• Confidence level interpretation is more important than the formula memorization alone.
• Errors in “accepting the null” wording are heavily penalized.

How you can support

• Walk the four steps: state, plan (conditions), do, conclude in context.
• Ask them to state H₀ and Hₐ in symbols and in words about the population.
• Have them check Random, 10%, and Large Counts before computing.
• Celebrate a correct confidence-interval interpretation sentence.
• Ask what a small p-value means for the claim in the story.
• Keep conclusions about the population parameter, not “the sample is true.”

What not to do

• Do not jump to a calculator p-value without stating hypotheses and conditions.
• Do not say “we accept H₀”—say fail to reject / not enough evidence.
• Do not interpret a 95% CI as “95% chance the interval caught this sample’s p̂.”
• Do not skip conditions because the calculator produced a number.
• Do not confuse one-proportion with two-proportion procedures.