The quick method. The quick method of Chapter 3 (pages 42–43) uses

^p

± 1/

√

n as a rough recipe for a 95% confidence interval for a population proportion.

The margin of error from the quick method is a bit larger than needed.

It differs most from the more accurate method of this chapter when ^p is close to 0 or 1. An SRS of 500 motorcycle registrations finds that 68 of the motorcycles are Harley-Davidsons. Give a 95% confidence interval for the proportion of all motorcycles that are Harleys by the quick method and then by the method of this chapter. How much larger is the quick-method margin of error?