6.1 Introducing Statistics: Why Be Normal?

Part of Inference for Categorical Data: Proportions in AP® Statistics. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

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The Logic of Statistical Inference

Statistical inference

The big question: How confident can we be that our sample statistic is close to the true population parameter?

Two main tools of inference:

Confidence intervals — estimate a parameter with a range of plausible values
Hypothesis tests — assess evidence for or against a claim about a parameter

Why normal? When conditions are met, the sampling distribution of ${\hat{p}}$ is approximately normal. This means we can use the standard normal distribution ( ${z}$ -scores) to quantify how unusual an observed statistic is.

Key insight: Inference is not magic — it's based on probability. We use the sampling distribution to determine what values of the statistic are likely vs. unlikely.

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