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Here is the problem: In a sample of 1000, 540 say yes. Find the 95 percent confidence interval for the proportion.

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Build a 95 percent confidence interval for the population proportion p.

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Sample proportion.

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Standard error.

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Critical value for 95 percent confidence. The middle 95 percent leaves 2.5 percent in each tail. Large-sample condition met: np̂ approximately 540 and n(1 minus p̂) approximately 460 are both at least 10.

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Margin of error.

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Interval: estimate plus or minus margin.

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So the answer is 95 percent CI: (0.50911, 0.57089); margin of error 0.0308904.

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We are 95 percent confident that the population proportion p lies between 0.50911 and 0.57089. The confidence describes the method: about 95 percent of intervals built this way from repeated samples would capture the true value.

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The interval is centred on the estimate: (0.50911 plus 0.57089) / 2 equals 0.54.

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Large-sample condition met: np̂ approximately 540 and n(1 minus p̂) approximately 460 are both at least 10.