6.4 Setting Up a Test for a Population Proportion

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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Writing Hypotheses

The null hypothesis ${H_0}$ : A specific claim about the parameter (always has an "=" sign)

H_0: p = p_0

where

{p_0}

is the claimed value.

The alternative hypothesis ${H_a}$ : Reflects what we're investigating:

${H_a: p > p_0}$ (one-sided, right-tailed)
${H_a: p < p_0}$ (one-sided, left-tailed)
${H_a: p \neq p_0}$ (two-sided)

Rules for writing hypotheses:

${H_0}$ and ${H_a}$ are about the population parameter ${p}$ , not the sample statistic ${\hat{p}}$
State hypotheses before looking at the data
Use the context to determine if one-sided or two-sided is appropriate

Example: A political party claims support from a majority (more than 50%) of voters.

H_0: p = 0.50 \quad H_a: p > 0.50

In this unit

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