## Confidence interval for a proportion, Applied Statistics

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The quick method for a confidence interval for a proportion uses

as an approximation for a 95% confidence interval.  The margin of error in this case is slightly larger than necessary.  Suppose that a simple random sample of 500 motorcycle registrations finds that 68 of the motorcycles are Yamahas.  Give a 95% confidence interval for the proportion of motorcycles in the population that are Yamahas using the quick method of chapter 3 and then by the more precise method of chapter 21.

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