AP Statistics / Unit 3: Inference for Categorical Data: Proportions
3.4 Justifying a Claim Based on a Confidence Interval for a Population Proportion
Notes
Interpret: "We are 95% confident that the interval from __ to __ captures the true proportion of [context]."
- A claimed value inside the interval is plausible; outside, it's not.
- 95% confidence means about 95% of such intervals capture $p$.
Practice
A 95% CI for $p$ is (0.42, 0.51). Is $p=0.5$ plausible?
Inside means plausible.
Using that interval, is $p=0.55$ plausible?
Outside the interval.
"95% confident" means:
Confidence describes the method's long-run success.
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