Common Mistakes
Statistics · AP · Inference for Quantitative Data — Means
Focus
Setting Up a Test for a Population Mean
This topic is assessed on the AP Exam.
Frequent mistakes
### 1. Inference without conditions
What it looks/sounds like: Calculator p-value or CI is reported with no plan step.
Why it happens: Conditions feel optional on technology items.
How to fix: Always state Random, 10%, and Large Counts/Normality as applicable.
### 2. Paired vs two-sample
What it looks/sounds like: Two-sample t is used on paired data.
Why it happens: Design structure is ignored.
How to fix: Use paired/one-sample on differences when matched.
### 3. z instead of t
What it looks/sounds like: z procedures used when σ is unknown.
Why it happens: Procedure choice is automatic.
How to fix: Use t when σ is unknown and conditions hold.
### 4. Correct work, wrong question
What it looks/sounds like: The algebra is fine but answers a different quantity than the stem asks for.
Why it happens: Attention locks onto the first operation instead of the final ask.
How to fix: Underline the final question; after solving, verify the boxed answer matches it.
### 5. Notation and justification gaps
What it looks/sounds like: Missing units, limit language, or ‘because’ statements AP graders expect.
Why it happens: Notation is treated as decoration rather than part of the score.
How to fix: Add one justification phrase per major step (definition, theorem, or rule).
How to avoid them
1. Identify paired vs independent samples. 2. State μ or μ_d clearly. 3. Mention practical vs statistical significance when relevant.
Quick self-check
- [ ] Can choose the correct t-procedure
- [ ] Can interpret a mean CI in context
- [ ] Can state t conditions