Assumptions for Inference

AP Statistics

The “Big Three” Assumptions

Before performing a t-test or z-test, we must check:

1. Random: Data must come from a random sample or randomized experiment.
2. Independent: The \(10\%\) condition (\(n \le 0.10N\)) when sampling without replacement.
3. Normal/Large Sample: * Means: \(n \ge 30\) or population is normal.
   • Proportions: \(np \ge 10\) and \(n(1-p) \ge 10\).

Why do we check?

“To generalize our results to a larger population, we must ensure our sample is representative and our sampling distribution is approximately Normal.”

Normal Condition for Means

If \(n < 30\) and we don’t know the population distribution: * Check the sample data for strong skewness or outliers. * Plot a histogram or Normal Probability Plot.