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Construct and interpret confidence intervals for a population proportion.
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A confidence interval gives a range of plausible values for a population parameter.
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Avoid these 3 frequent errors
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where:
| Confidence Level | |
|---|---|
| 90% | 1.645 |
| 95% | 1.960 |
| 99% | 2.576 |
Correct: "We are [C]% confident that the true proportion of [context] is between [lower bound] and [upper bound]."
Incorrect: "There is a [C]% probability that is in this interval." (The parameter is fixed; the interval either contains it or it doesn't.)
If we repeated the sampling process many times, approximately 95% of the resulting confidence intervals would contain the true population proportion .
The margin of error decreases when:
To achieve a desired margin of error with confidence level :
If is unknown, use for the most conservative (largest) sample size.
AP Tip: You MUST check all three conditions (Random, 10%, Large Counts) and interpret the interval in context to receive full credit on free-response questions.