Inference for Quantitative Data: Means — AP Statistics
1. Unit at a Glance
This unit extends the core inference foundations you learned for proportions to quantitative data, where the population standard deviation is almost never known. Instead of using the standard normal z-distribution, we rely on the t-distribution, which accounts for additional uncertainty from estimating the population standard deviation with the sample standard deviation.
We progress from foundational concepts to applied inference: starting with understanding the t-distribution itself, moving to inference for a single population mean, then comparing two means for paired and independent study designs. All topics align with AP exam expectations for multiple choice and free response questions.
Common Pitfalls
Why: The z-distribution does not account for the extra uncertainty from estimating $σ$ with $s$.
Why: Paired data are dependent, so analyzing two separate samples leads to an incorrect standard error.
Why: The standard deviation uses the unknown population $σ$, while standard error uses the sample $s$ you calculate from data.