6.2 Constructing a Confidence Interval 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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One-Proportion z Confidence Interval

Conditions (PANIC acronym):

Parameter: Identify the parameter of interest ( ${p}$ = true proportion of...)
Assumptions: Check conditions
- Random: Sample is a random sample
- Independence: ${n < 10\%}$ of population
- Normal: ${n\hat{p} \geq 10}$ AND ${n(1-\hat{p}) \geq 10}$ (use ${\hat{p}}$ not ${p}$ !)
Name the interval: One-proportion z interval
Interval: Compute
Conclusion: Interpret in context

Formula:

\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}

where ${z^*}$ is the critical value for the desired confidence level.

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