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Confidence Interval for a Population Proportion (z-interval)

p̂ ± z* · √(p̂(1−p̂)/n). Use z* for confidence level. Conditions: SRS, np̂ ≥ 10, n(1−p̂) ≥ 10.

StatisticsCommon Core UNC-4.BINFVerified correct ✓

Worked examples

In a survey of n = 100 people, 70 responded yes, giving a sample proportion p̂ = 0.70. Construct a 99% confidence interval for the population proportion. (Use z* = 2.576.) What is the margin of error? Give your answer rounded to 4 decimal places.
Answer: 0.118
In a survey of n = 500 people, 350 responded yes, giving a sample proportion p̂ = 0.70. Construct a 95% confidence interval for the population proportion. (Use z* = 1.96.) What is the margin of error? Give your answer rounded to 4 decimal places.
Answer: 0.0402

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